11 x1 t10 01 graphing quadratics (2013)

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The Quadratic Polynomial and the Parabola

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Page 1: 11 x1 t10 01 graphing quadratics (2013)

The Quadratic Polynomial and the Parabola

Page 2: 11 x1 t10 01 graphing quadratics (2013)

The Quadratic Polynomial and the Parabola

Quadratic polynomial –

Page 3: 11 x1 t10 01 graphing quadratics (2013)

The Quadratic Polynomial and the Parabola

Quadratic polynomial – 2ax bx c

Page 4: 11 x1 t10 01 graphing quadratics (2013)

The Quadratic Polynomial and the Parabola

Quadratic polynomial – 2ax bx c

Quadratic function –

Page 5: 11 x1 t10 01 graphing quadratics (2013)

The Quadratic Polynomial and the Parabola

Quadratic polynomial – 2ax bx c

Quadratic function – 2y ax bx c

Page 6: 11 x1 t10 01 graphing quadratics (2013)

The Quadratic Polynomial and the Parabola

Quadratic polynomial – 2ax bx c

Quadratic function – 2y ax bx c

Quadratic equation –

Page 7: 11 x1 t10 01 graphing quadratics (2013)

The Quadratic Polynomial and the Parabola

Quadratic polynomial – 2ax bx c

Quadratic function – 2y ax bx c

Quadratic equation – 2 0ax bx c

Page 8: 11 x1 t10 01 graphing quadratics (2013)

The Quadratic Polynomial and the Parabola

Quadratic polynomial – 2ax bx c

Quadratic function – 2y ax bx c

Quadratic equation – 2 0ax bx c Coefficients –

Page 9: 11 x1 t10 01 graphing quadratics (2013)

The Quadratic Polynomial and the Parabola

Quadratic polynomial – 2ax bx c

Quadratic function – 2y ax bx c

Quadratic equation – 2 0ax bx c , ,a b cCoefficients –

Page 10: 11 x1 t10 01 graphing quadratics (2013)

The Quadratic Polynomial and the Parabola

Quadratic polynomial – 2ax bx c

Quadratic function – 2y ax bx c

Quadratic equation – 2 0ax bx c , ,a b cCoefficients –

Indeterminate –

Page 11: 11 x1 t10 01 graphing quadratics (2013)

The Quadratic Polynomial and the Parabola

Quadratic polynomial – 2ax bx c

Quadratic function – 2y ax bx c

Quadratic equation – 2 0ax bx c , ,a b cCoefficients –xIndeterminate –

Page 12: 11 x1 t10 01 graphing quadratics (2013)

The Quadratic Polynomial and the Parabola

Quadratic polynomial – 2ax bx c

Quadratic function – 2y ax bx c

Quadratic equation – 2 0ax bx c , ,a b cCoefficients –xIndeterminate –

Roots –

Page 13: 11 x1 t10 01 graphing quadratics (2013)

The Quadratic Polynomial and the Parabola

Quadratic polynomial – 2ax bx c

Quadratic function – 2y ax bx c

Quadratic equation – 2 0ax bx c , ,a b cCoefficients –xIndeterminate –

Roots – Solutions to the quadratic equation

Page 14: 11 x1 t10 01 graphing quadratics (2013)

The Quadratic Polynomial and the Parabola

Quadratic polynomial – 2ax bx c

Quadratic function – 2y ax bx c

Quadratic equation – 2 0ax bx c , ,a b cCoefficients –xIndeterminate –

Roots – Solutions to the quadratic equationZeroes –

Page 15: 11 x1 t10 01 graphing quadratics (2013)

The Quadratic Polynomial and the Parabola

Quadratic polynomial – 2ax bx c

Quadratic function – 2y ax bx c

Quadratic equation – 2 0ax bx c , ,a b cCoefficients –xIndeterminate –

Roots – Solutions to the quadratic equationZeroes – x intercepts of the quadratic function

Page 16: 11 x1 t10 01 graphing quadratics (2013)

The Quadratic Polynomial and the Parabola

Quadratic polynomial – 2ax bx c

Quadratic function – 2y ax bx c

Quadratic equation – 2 0ax bx c , ,a b cCoefficients –xIndeterminate –

Roots – Solutions to the quadratic equationZeroes – x intercepts of the quadratic function

2e.g. Find the roots of 1 0x

Page 17: 11 x1 t10 01 graphing quadratics (2013)

The Quadratic Polynomial and the Parabola

Quadratic polynomial – 2ax bx c

Quadratic function – 2y ax bx c

Quadratic equation – 2 0ax bx c , ,a b cCoefficients –xIndeterminate –

Roots – Solutions to the quadratic equationZeroes – x intercepts of the quadratic function

2e.g. Find the roots of 1 0x 2

2

1 01

xx

Page 18: 11 x1 t10 01 graphing quadratics (2013)

The Quadratic Polynomial and the Parabola

Quadratic polynomial – 2ax bx c

Quadratic function – 2y ax bx c

Quadratic equation – 2 0ax bx c , ,a b cCoefficients –xIndeterminate –

Roots – Solutions to the quadratic equationZeroes – x intercepts of the quadratic function

2e.g. Find the roots of 1 0x 2

2

1 01

xx

1x

Page 19: 11 x1 t10 01 graphing quadratics (2013)

The Quadratic Polynomial and the Parabola

Quadratic polynomial – 2ax bx c

Quadratic function – 2y ax bx c

Quadratic equation – 2 0ax bx c , ,a b cCoefficients –xIndeterminate –

Roots – Solutions to the quadratic equationZeroes – x intercepts of the quadratic function

2e.g. Find the roots of 1 0x 2

2

1 01

xx

1x the roots are 1 and 1x x

Page 20: 11 x1 t10 01 graphing quadratics (2013)

Graphing Quadratics

Page 21: 11 x1 t10 01 graphing quadratics (2013)

Graphing QuadraticsThe graph of a quadratic function is a parabola.

Page 22: 11 x1 t10 01 graphing quadratics (2013)

Graphing QuadraticsThe graph of a quadratic function is a parabola. 2y ax bx c

Page 23: 11 x1 t10 01 graphing quadratics (2013)

Graphing QuadraticsThe graph of a quadratic function is a parabola. 2y ax bx c

a

Page 24: 11 x1 t10 01 graphing quadratics (2013)

Graphing QuadraticsThe graph of a quadratic function is a parabola. 2y ax bx c

ay

x

Page 25: 11 x1 t10 01 graphing quadratics (2013)

Graphing QuadraticsThe graph of a quadratic function is a parabola. 2y ax bx c

ay

x0a

Page 26: 11 x1 t10 01 graphing quadratics (2013)

Graphing QuadraticsThe graph of a quadratic function is a parabola. 2y ax bx c

ay

x0a

concave up

Page 27: 11 x1 t10 01 graphing quadratics (2013)

Graphing QuadraticsThe graph of a quadratic function is a parabola. 2y ax bx c

ay

x0a

concave up

y

x

Page 28: 11 x1 t10 01 graphing quadratics (2013)

Graphing QuadraticsThe graph of a quadratic function is a parabola. 2y ax bx c

ay

x0a

concave up0a

y

x

Page 29: 11 x1 t10 01 graphing quadratics (2013)

Graphing QuadraticsThe graph of a quadratic function is a parabola. 2y ax bx c

ay

x0a

concave up0a

y

x

concave down

Page 30: 11 x1 t10 01 graphing quadratics (2013)

Graphing QuadraticsThe graph of a quadratic function is a parabola. 2y ax bx c

ay

x0a

concave up0a

y

x

concave downc

Page 31: 11 x1 t10 01 graphing quadratics (2013)

Graphing QuadraticsThe graph of a quadratic function is a parabola. 2y ax bx c

ay

x0a

concave up0a

y

x

concave downc = y intercept

Page 32: 11 x1 t10 01 graphing quadratics (2013)

Graphing QuadraticsThe graph of a quadratic function is a parabola. 2y ax bx c

ay

x0a

concave up0a

y

x

concave downc = y interceptzeroes (roots)

Page 33: 11 x1 t10 01 graphing quadratics (2013)

Graphing QuadraticsThe graph of a quadratic function is a parabola. 2y ax bx c

ay

x0a

concave up0a

y

x

concave downc = y interceptzeroes (roots) = x intercepts

Page 34: 11 x1 t10 01 graphing quadratics (2013)

Graphing QuadraticsThe graph of a quadratic function is a parabola. 2y ax bx c

ay

x0a

concave up0a

y

x

concave downc = y interceptzeroes (roots) = x intercepts

2bxa

Page 35: 11 x1 t10 01 graphing quadratics (2013)

Graphing QuadraticsThe graph of a quadratic function is a parabola. 2y ax bx c

ay

x0a

concave up0a

y

x

concave downc = y interceptzeroes (roots) = x intercepts

2bxa

= axis of symmetry

Page 36: 11 x1 t10 01 graphing quadratics (2013)

Graphing QuadraticsThe graph of a quadratic function is a parabola. 2y ax bx c

ay

x0a

concave up0a

y

x

concave downc = y interceptzeroes (roots) = x intercepts

2bxa

= axis of symmetry Note: AOS is the average of the zeroes

Page 37: 11 x1 t10 01 graphing quadratics (2013)

Graphing QuadraticsThe graph of a quadratic function is a parabola. 2y ax bx c

ay

x0a

concave up0a

y

x

concave downc = y interceptzeroes (roots) = x intercepts

2bxa

= axis of symmetry Note: AOS is the average of the zeroes

vertex

Page 38: 11 x1 t10 01 graphing quadratics (2013)

Graphing QuadraticsThe graph of a quadratic function is a parabola. 2y ax bx c

ay

x0a

concave up0a

y

x

concave downc = y interceptzeroes (roots) = x intercepts

2bxa

= axis of symmetry Note: AOS is the average of the zeroes

vertex x value is the AOS

Page 39: 11 x1 t10 01 graphing quadratics (2013)

Graphing QuadraticsThe graph of a quadratic function is a parabola. 2y ax bx c

ay

x0a

concave up0a

y

x

concave downc = y interceptzeroes (roots) = x intercepts

2bxa

= axis of symmetry Note: AOS is the average of the zeroes

vertex x value is the AOSy value is found by substituting AOS into the function.

Page 40: 11 x1 t10 01 graphing quadratics (2013)

Graphing QuadraticsThe graph of a quadratic function is a parabola. 2y ax bx c

ay

x0a

concave up0a

y

x

concave downc = y interceptzeroes (roots) = x intercepts

2bxa

= axis of symmetry Note: AOS is the average of the zeroes

vertex x value is the AOSy value is found by substituting AOS into the function.

(It is the maximum/minimum value of the function)

Page 41: 11 x1 t10 01 graphing quadratics (2013)

e.g. 2Graph 8 12y x x

Page 42: 11 x1 t10 01 graphing quadratics (2013)

e.g. 2Graph 8 12y x x a = 1 > 0

y

x

Page 43: 11 x1 t10 01 graphing quadratics (2013)

e.g. 2Graph 8 12y x x a = 1 > 0 concave up

y

x

Page 44: 11 x1 t10 01 graphing quadratics (2013)

e.g. 2Graph 8 12y x x a = 1 > 0 concave up c = 12

y

x

2 8 12y x x

Page 45: 11 x1 t10 01 graphing quadratics (2013)

e.g. 2Graph 8 12y x x a = 1 > 0 concave up c = 12 intercept is 0,12y

y

x

Page 46: 11 x1 t10 01 graphing quadratics (2013)

e.g. 2Graph 8 12y x x a = 1 > 0 concave up c = 12 intercept is 0,12y

y

x

12

Page 47: 11 x1 t10 01 graphing quadratics (2013)

e.g. 2Graph 8 12y x x a = 1 > 0 concave up c = 12 intercept is 0,12y

zeroes y

x

12

Page 48: 11 x1 t10 01 graphing quadratics (2013)

e.g. 2Graph 8 12y x x a = 1 > 0 concave up c = 12 intercept is 0,12y

zeroes 2 8 12 0x x y

x

12

2 8 12y x x

Page 49: 11 x1 t10 01 graphing quadratics (2013)

e.g. 2Graph 8 12y x x a = 1 > 0 concave up c = 12 intercept is 0,12y

zeroes 2 8 12 0x x 6 2 0x x

y

x

12

2 8 12y x x

Page 50: 11 x1 t10 01 graphing quadratics (2013)

e.g. 2Graph 8 12y x x a = 1 > 0 concave up c = 12 intercept is 0,12y

zeroes 2 8 12 0x x 6 2 0x x

6 or 2x x

y

x

12

2 8 12y x x

Page 51: 11 x1 t10 01 graphing quadratics (2013)

e.g. 2Graph 8 12y x x a = 1 > 0 concave up c = 12 intercept is 0,12y

zeroes 2 8 12 0x x 6 2 0x x

6 or 2x x

intercepts are

6,0 and 2,0x

y

x

12

2 8 12y x x

Page 52: 11 x1 t10 01 graphing quadratics (2013)

e.g. 2Graph 8 12y x x a = 1 > 0 concave up c = 12 intercept is 0,12y

zeroes 2 8 12 0x x 6 2 0x x

6 or 2x x

intercepts are

6,0 and 2,0x

y

x

12

–2 –6

2 8 12y x x

Page 53: 11 x1 t10 01 graphing quadratics (2013)

e.g. 2Graph 8 12y x x a = 1 > 0 concave up c = 12 intercept is 0,12y

zeroes 2 8 12 0x x 6 2 0x x

6 or 2x x

intercepts are

6,0 and 2,0x

AOS

y

x

12

–2 –6

2 8 12y x x

Page 54: 11 x1 t10 01 graphing quadratics (2013)

e.g. 2Graph 8 12y x x a = 1 > 0 concave up c = 12 intercept is 0,12y

zeroes 2 8 12 0x x 6 2 0x x

6 or 2x x

intercepts are

6,0 and 2,0x

AOS2

bxa

y

x

12

–2 –6

2 8 12y x x

Page 55: 11 x1 t10 01 graphing quadratics (2013)

e.g. 2Graph 8 12y x x a = 1 > 0 concave up c = 12 intercept is 0,12y

zeroes 2 8 12 0x x 6 2 0x x

6 or 2x x

intercepts are

6,0 and 2,0x

AOS2

bxa

824

y

x

12

–2 –6

2 8 12y x x

Page 56: 11 x1 t10 01 graphing quadratics (2013)

e.g. 2Graph 8 12y x x a = 1 > 0 concave up c = 12 intercept is 0,12y

zeroes 2 8 12 0x x 6 2 0x x

6 or 2x x

intercepts are

6,0 and 2,0x

AOS2

bxa

824

OR6 22

x

y

x

12

–2 –6

2 8 12y x x

Page 57: 11 x1 t10 01 graphing quadratics (2013)

e.g. 2Graph 8 12y x x a = 1 > 0 concave up c = 12 intercept is 0,12y

zeroes 2 8 12 0x x 6 2 0x x

6 or 2x x

intercepts are

6,0 and 2,0x

AOS2

bxa

824

OR6 22

x

4

y

x

12

–2 –6

2 8 12y x x

Page 58: 11 x1 t10 01 graphing quadratics (2013)

e.g. 2Graph 8 12y x x a = 1 > 0 concave up c = 12 intercept is 0,12y

zeroes 2 8 12 0x x 6 2 0x x

6 or 2x x

intercepts are

6,0 and 2,0x

AOS2

bxa

824

OR6 22

x

4

y

x

12

–2 –6

2 8 12y x x

Page 59: 11 x1 t10 01 graphing quadratics (2013)

e.g. 2Graph 8 12y x x a = 1 > 0 concave up c = 12 intercept is 0,12y

zeroes 2 8 12 0x x 6 2 0x x

6 or 2x x

intercepts are

6,0 and 2,0x

AOS2

bxa

824

OR6 22

x

4

vertex

y

x

12

–2 –6

2 8 12y x x

Page 60: 11 x1 t10 01 graphing quadratics (2013)

e.g. 2Graph 8 12y x x a = 1 > 0 concave up c = 12 intercept is 0,12y

zeroes 2 8 12 0x x 6 2 0x x

6 or 2x x

intercepts are

6,0 and 2,0x

AOS2

bxa

824

OR6 22

x

4

vertex 24 8 4 12y

y

x

12

–2 –6

2 8 12y x x

Page 61: 11 x1 t10 01 graphing quadratics (2013)

e.g. 2Graph 8 12y x x a = 1 > 0 concave up c = 12 intercept is 0,12y

zeroes 2 8 12 0x x 6 2 0x x

6 or 2x x

intercepts are

6,0 and 2,0x

AOS2

bxa

824

OR6 22

x

4

vertex 24 8 4 12y

4

y

x

12

–2 –6

2 8 12y x x

Page 62: 11 x1 t10 01 graphing quadratics (2013)

e.g. 2Graph 8 12y x x a = 1 > 0 concave up c = 12 intercept is 0,12y

zeroes 2 8 12 0x x 6 2 0x x

6 or 2x x

intercepts are

6,0 and 2,0x

AOS2

bxa

824

OR6 22

x

4

vertex 24 8 4 12y

4 vertex is 4, 4

y

x

12

–2 –6

2 8 12y x x

Page 63: 11 x1 t10 01 graphing quadratics (2013)

e.g. 2Graph 8 12y x x a = 1 > 0 concave up c = 12 intercept is 0,12y

zeroes 2 8 12 0x x 6 2 0x x

6 or 2x x

intercepts are

6,0 and 2,0x

AOS2

bxa

824

OR6 22

x

4

vertex 24 8 4 12y

4 vertex is 4, 4

y

x

12

–2 –6

(–4, –4)

2 8 12y x x

Page 64: 11 x1 t10 01 graphing quadratics (2013)

e.g. 2Graph 8 12y x x a = 1 > 0 concave up c = 12 intercept is 0,12y

zeroes 2 8 12 0x x 6 2 0x x

6 or 2x x

intercepts are

6,0 and 2,0x

AOS2

bxa

824

OR6 22

x

4

vertex 24 8 4 12y

4 vertex is 4, 4

y

x

12

–2 –6

(–4, –4)

2 8 12y x x

Page 65: 11 x1 t10 01 graphing quadratics (2013)

(ii) Find the quadratic with;a) roots 3 and 6

Page 66: 11 x1 t10 01 graphing quadratics (2013)

(ii) Find the quadratic with;a) roots 3 and 6

2 9 18y a x x

Page 67: 11 x1 t10 01 graphing quadratics (2013)

(ii) Find the quadratic with;a) roots 3 and 6

2 9 18y a x x

6 3 6 3

Page 68: 11 x1 t10 01 graphing quadratics (2013)

(ii) Find the quadratic with;a) roots 3 and 6

2 9 18y a x x

6 3 6 3

b) monic roots 3 2 and 3 2

Page 69: 11 x1 t10 01 graphing quadratics (2013)

(ii) Find the quadratic with;a) roots 3 and 6

2 9 18y a x x

6 3 6 3

b) monic roots 3 2 and 3 2 2 6 7y x x

c) roots 2 and 8 and vertex (5,3)

2 10 16y a x x

25,3 : 3 5 10 5 16a

3 913

a

a

21 10 163

y x x

Page 70: 11 x1 t10 01 graphing quadratics (2013)

(ii) Find the quadratic with;a) roots 3 and 6

2 9 18y a x x

6 3 6 3

b) monic roots 3 2 and 3 2 2 6 7y x x

3 2 3 2 3 2 3 2

Page 71: 11 x1 t10 01 graphing quadratics (2013)

(ii) Find the quadratic with;a) roots 3 and 6

2 9 18y a x x

6 3 6 3

b) monic roots 3 2 and 3 2 2 6 7y x x

3 2 3 2 3 2 3 2 c) roots 2 and 8 and vertex (5,3)

Page 72: 11 x1 t10 01 graphing quadratics (2013)

(ii) Find the quadratic with;a) roots 3 and 6

2 9 18y a x x

6 3 6 3

b) monic roots 3 2 and 3 2 2 6 7y x x

3 2 3 2 3 2 3 2 c) roots 2 and 8 and vertex (5,3)

2 10 16y a x x

Page 73: 11 x1 t10 01 graphing quadratics (2013)

(ii) Find the quadratic with;a) roots 3 and 6

2 9 18y a x x

6 3 6 3

b) monic roots 3 2 and 3 2 2 6 7y x x

3 2 3 2 3 2 3 2 c) roots 2 and 8 and vertex (5,3)

2 10 16y a x x

25,3 : 3 5 10 5 16a

Page 74: 11 x1 t10 01 graphing quadratics (2013)

(ii) Find the quadratic with;a) roots 3 and 6

2 9 18y a x x

6 3 6 3

b) monic roots 3 2 and 3 2 2 6 7y x x

3 2 3 2 3 2 3 2 c) roots 2 and 8 and vertex (5,3)

2 10 16y a x x

25,3 : 3 5 10 5 16a

3 913

a

a

Page 75: 11 x1 t10 01 graphing quadratics (2013)

(ii) Find the quadratic with;a) roots 3 and 6

2 9 18y a x x

6 3 6 3

b) monic roots 3 2 and 3 2 2 6 7y x x

3 2 3 2 3 2 3 2 c) roots 2 and 8 and vertex (5,3)

2 10 16y a x x

25,3 : 3 5 10 5 16a

3 913

a

a

21 10 163

y x x

Page 76: 11 x1 t10 01 graphing quadratics (2013)

(iii) Solve;2) 5 6 0a x x

Page 77: 11 x1 t10 01 graphing quadratics (2013)

(iii) Solve;2) 5 6 0a x x

2 3 0x x

Page 78: 11 x1 t10 01 graphing quadratics (2013)

(iii) Solve;2) 5 6 0a x x

2 3 0x x

y

x–3 –2

Page 79: 11 x1 t10 01 graphing quadratics (2013)

(iii) Solve;2) 5 6 0a x x

2 3 0x x

y

x–3 –2

Page 80: 11 x1 t10 01 graphing quadratics (2013)

(iii) Solve;2) 5 6 0a x x

2 3 0x x

y

x–3 –2 Q: for what values of x is the

parabola above the x axis?

Page 81: 11 x1 t10 01 graphing quadratics (2013)

(iii) Solve;2) 5 6 0a x x

2 3 0x x

y

x–3 –2 Q: for what values of x is the

parabola above the x axis?

Page 82: 11 x1 t10 01 graphing quadratics (2013)

(iii) Solve;2) 5 6 0a x x

2 3 0x x

y

x–3 –2 Q: for what values of x is the

parabola above the x axis?

3 or 2x x

Page 83: 11 x1 t10 01 graphing quadratics (2013)

(iii) Solve;2) 5 6 0a x x

2 3 0x x

y

x–3 –2 Q: for what values of x is the

parabola above the x axis?

3 or 2x x

2) 3 4b x x

Page 84: 11 x1 t10 01 graphing quadratics (2013)

(iii) Solve;2) 5 6 0a x x

2 3 0x x

y

x–3 –2 Q: for what values of x is the

parabola above the x axis?

3 or 2x x

2) 3 4b x x 2 3 4 0x x

Page 85: 11 x1 t10 01 graphing quadratics (2013)

(iii) Solve;2) 5 6 0a x x

2 3 0x x

y

x–3 –2 Q: for what values of x is the

parabola above the x axis?

3 or 2x x

2) 3 4b x x

4 1 0x x

2 3 4 0x x

Page 86: 11 x1 t10 01 graphing quadratics (2013)

(iii) Solve;2) 5 6 0a x x

2 3 0x x

y

x–3 –2 Q: for what values of x is the

parabola above the x axis?

3 or 2x x

2) 3 4b x x

4 1 0x x

y

x1–4

2 3 4 0x x

Page 87: 11 x1 t10 01 graphing quadratics (2013)

(iii) Solve;2) 5 6 0a x x

2 3 0x x

y

x–3 –2 Q: for what values of x is the

parabola above the x axis?

3 or 2x x

2) 3 4b x x

4 1 0x x

y

x1–4

2 3 4 0x x

Page 88: 11 x1 t10 01 graphing quadratics (2013)

(iii) Solve;2) 5 6 0a x x

2 3 0x x

y

x–3 –2 Q: for what values of x is the

parabola above the x axis?

3 or 2x x

2) 3 4b x x

4 1 0x x

y

x1–4

Q: for what values of x is theparabola below the x axis?

2 3 4 0x x

Page 89: 11 x1 t10 01 graphing quadratics (2013)

(iii) Solve;2) 5 6 0a x x

2 3 0x x

y

x–3 –2 Q: for what values of x is the

parabola above the x axis?

3 or 2x x

2) 3 4b x x

4 1 0x x

y

x1–4

Q: for what values of x is theparabola below the x axis?

2 3 4 0x x

Page 90: 11 x1 t10 01 graphing quadratics (2013)

(iii) Solve;2) 5 6 0a x x

2 3 0x x

y

x–3 –2 Q: for what values of x is the

parabola above the x axis?

3 or 2x x

2) 3 4b x x

4 1 0x x

y

x1–4

Q: for what values of x is theparabola below the x axis?

4 1x

2 3 4 0x x

Page 91: 11 x1 t10 01 graphing quadratics (2013)

Exercise 8A; 1adf, 2adf, 3bd, 4bd, 5c, 6ade, 7d, 9ace, 12c,13b, 14a