Warm ups Graph completely (with all parts from worksheet)

2 2 8y x x

11-2 Solving Quadratic Equations by Graphing

Objective: To find the roots of a quadratic equation.

Standard 21.0

Homework Questions?

View Answer Key

Example 1

Let’s use the warm up problem!

Look at where the parabola crosses the x axis… These points are the ROOTS!

The roots are the x-intercepts. Look at your warmup graph… where does it cross the x axis?

2 2 8y x x

Look at the roots..

How else did we learn how to solve these? Factoring!

2 2 8 0x x

( 4)( 2) 0x x

4 0x 2 0x

{ 4,2}

What are the roots?

Roots can look like…2 roots 1 root No real roots

ROOTS FOR TOO #2 are like this

Does not fall on a nice, whole numberBetween 2 numbers: write as inequality

Start all the way to the left Write with “<“ signs “x” in the middle of the 2 #’s

2 < x < 3

6 < x < 7

TOO – BAD slide.Solve by graphing.

2 2 3 0x x

2 9 5 0x x

2 12 36 0x x

2 2 5 0x x

{ 1,3}

{ 9 8, 1 0}x x

{6, . .}D R

noREALroots

: (1, 4)vertex

: ( 4.5, 15.25)vertex

: (6,0)vertex

Roots

1.

2.

3.

4.

: ( 1, 4)vertex

Estimate if not exact. If not sure if it is exact, then try to factor!

Vertex in on x-axis

Does not cross x-axis

Example 2

Graph given roots {-2,0} and minimum (-1,-1)

Vertex!!

RECAP OF ROOTS

2 Roots Crosses x-axis twice Vertex is below and opens

up Vertex is above and opens

down Whole Numbers

Answer: (x,0) and (x,0) Between 2 Numbers

Answer: # < x < # # < x <

#

1 Root Vertex is on the x-axis Answer is vertex!

(x,0) No Roots

Does not cross x-axis Vertex is above and

opens up Vertex is below and

opens down Answer: None

SIDE NOTE Y-intercept, x always equals 0 so . . .

EX#1 y = 1/2x2 – 2x + 2

y = 1/2(0)2 – 2(0) + 2

y = 0 – 0 + 2

y = 2

(0,2) y-intercept

Y-intercept is ALWAYS “c”

Ex: y = 2x2 – 5x + 26

(0,26)

EX #2 y = -x2 – 2x + 3y = -(0)2 – 2(0) + 3y = 0 – 0 + 3y = 3(0,3) y-intercept

Homework

Pg. 625 # 17-19, 20-23, 35-38 Graph the parabola first, THEN see where it

crosses the x-axis. The point(s) at which it crosses (once, twice, or

none) are the roots. Write the roots in brackets { } Use graph paper!

Math Lab Warmup: Simplify22 4 3x x

1x

3x

1

2x

2x

Simplify 213 1

2x x

1x

3x

1

2x

2x

Review

Commonly missed test questions: factor.

225 81x 22 16 30x x

Review

Commonly missed test questions: factor.

225 20 4x x 22 3x x

Review

Commonly missed test questions: solve

2(5 3) 0x 249 144 0x

Review

Commonly missed test questions: solve

2 56x x 22 40x x

Homework Groups

Let’s get into the same homework groups that we worked on yesterday.

Once you are seated, raise your hand if you are all finished, or finish, your homework.

If you finish homework..

Either graph or solve using quad. Formula: Depending on what you’ve learned so far

22 4 3 0x x

2 2 5 0x x

2 6 9 0x x

22 4 1 0x x