notes 1 solving and graphing quadratics and more - … 1 solvin… · ·...

Notes #1 Quadratics: “Graphing, Solving and more! Name:________________________

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1.) 𝑮𝑹𝑨𝑷𝑯: 𝒚 = 𝒙𝟐 PLEASE COMPLETE THE NOTES ON MY WEBSITE FOR 1 AND 2

VERTEX: AXIS OF SYMMETRY X INTERCEPT DOMAIN: Solutions: Y INTERCEPT RANGE: A.) WHY DOES GRAPH 1 OPEN UP?

B.) WHAT PATTERN DO YOU NOTICE

ABOUT THE X VALUES IN THE TABLE

C.) WHAT DO YOU NOTICE ABOUT THE VERTEX?

x y= 𝑥! (x,y)


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2.) 𝑮𝑹𝑨𝑷𝑯: 𝒚 = −𝒙𝟐

VERTEX: AXIS OF SYMMETRY X INTERCEPT DOMAIN: Solutions: Y INTERCEPT RANGE: D.) WHY DOES GRAPH 1 OPEN DOWN?

E.) WHAT PATTERN DO YOU NOTICE

ABOUT THE X VALUES IN THE TABLE C.) WHAT DO YOU NOTICE ABOUT THE VERTEX?

x y= −𝑥! (x,y)


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3.) METHOD 1: T –CHART “I DO” GRAPH y= 𝒙𝟐 + 𝟐𝒙− 𝟑

VERTEX: AXIS OF SYMMETRY X INTERCEPT DOMAIN: Solutions: Y INTERCEPT

RANGE:

x y= 𝑥! + 2𝑥 − 3 (x,y) -‐3

-‐2

-‐1

0

1

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3


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3.) METHOD 2: FACTORING “I DO” GRAPH y= 𝒙𝟐 + 𝟐𝒙− 𝟑 BUT BEFORE WE DO LET’S…. Solve for x: 𝑥! + 2𝑥 − 3 What are the solution(s) of y= 𝑥! + 2𝑥 − 3 ? NOW GRAPH a.) Find the x intercepts/ ROOTS/ZEROS of y= 𝑥! + 2𝑥 − 3 b.) Find the y intercept (x = ) of y= 𝑥! + 2𝑥 − 3 c.) Find the VERTEX… Divides the parabola in half • Find the x value of the vertex: if you know the x intercepts, take the AVERAGE (_______________________________________________________) *****If you don’t know the x intercepts, use the formula x= • Now find the y value of the vertex: VERTEX: ( , )


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GRAPH y= 𝒙𝟐 + 𝟐𝒙− 𝟑 X intercept (s) Y intercept Vertex Axis of symmetry Domain Range

4.) METHOD 1: T –CHART “WE DO” GRAPH y= 𝒙𝟐 + 𝟔𝒙+ 𝟖

X intercept y intercept vertex axis of symmetry Domain Range

x y= 𝑥! + 6𝑥 + 8 (x,y) -‐3

-‐2

-‐1

0

1

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4.) METHOD 2: FACTORING “WE DO” GRAPH y= 𝒙𝟐 + 𝟔𝒙+ 𝟖 BUT BEFORE WE DO LET’S…. Solve for x: 𝑥! + 6𝑋 + 8 What are the solution(s) of y= 𝑥! + 6𝑥 + 8 ? NOW GRAPH a.) Find the x intercepts/ ROOTS/ZEROS of y= 𝑥! + 6𝑥 + 8

b.) Find the y intercept of y= 𝑥! + 6𝑥 + 8 c.) Find the VERTEX

GRAPH y= 𝒙𝟐 + 𝟔𝒙+ 𝟖 X intercept (s) Solution(s): Y intercept Vertex Axis of symmetry Domain Range


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5.) METHOD 1: T –CHART “YOU DO” GRAPH y= 𝒙𝟐 − 𝒙− 𝟐

X intercept y intercept vertex axis of symmetry Domain Range 5.) METHOD 2: FACTORING “YOU DO” GRAPH y= 𝒙𝟐 − 𝒙− 𝟐 Solve for x: 𝑥! − 𝑥 − 2 What are the solution(s) of y= 𝑥! − 𝑥 − 2 ?


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NOW GRAPH y= 𝑥! − 𝑥 − 2 a.) Find the x intercepts/ ROOTS/ZEROS

b.) Find the y intercept c.) Find the VERTEX

GRAPH y= 𝒙𝟐 − 𝒙− 𝟐 X intercept (s) Solution(s): Y intercept Vertex Axis of symmetry Domain Range 6.) METHOD 1: T –CHART “I DO” GRAPH y= 𝒙𝟐 − 𝟏


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6.) METHOD 2: FACTORING “I DO” GRAPH y= 𝒙𝟐 − 𝟏

BUT BEFORE WE DO LET’S…. Solve for x: 𝑥! − 1 What are the solution(s) of y= 𝑥! − 1 NOW GRAPH y= 𝑥! − 1 a.) Find the x intercepts/ ROOTS/ZEROS

b.) Find the y intercept of c.) Find the VERTEX

GRAPH y= 𝑥! − 1 X intercept (s) Solution(s): Y intercept Vertex Axis of symmetry Domain Range


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7.) METHOD 2: FACTORING “WE DO” GRAPH y= 𝒙𝟐 − 𝟒

BUT BEFORE WE DO LET’S…. Solve for x: 𝒙𝟐 − 𝟒 What are the solution(s) of y= 𝒙𝟐 − 𝟒 NOW GRAPH y= 𝒙𝟐 − 𝟒 a.) Find the x intercepts/ ROOTS/ZEROS


GRAPH y= 𝒙𝟐 − 𝟒 X intercept (s) Solution(s): Y intercept Vertex Axis of symmetry Domain Range


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8.) METHOD 2: FACTORING “YOU DO” GRAPH y= 𝟗𝒙𝟐 − 𝟏𝟔 BUT BEFORE WE DO LET’S….

Solve for x: 𝟗𝒙𝟐 − 𝟏𝟔 What are the solution(s) of y= 𝟗𝒙𝟐 − 𝟏𝟔

NOW GRAPH y= 𝟗𝒙𝟐 − 𝟏𝟔 a.) Find the x intercepts/ ROOTS/ZEROS


GRAPH y= 𝟗𝒙𝟐 − 𝟏𝟔 X intercept (s) Solution(s): Y intercept Vertex Axis of symmetry Domain Range


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9.) METHOD 2: FACTORING “I DO” GRAPH y= 𝒙𝟐 − 𝟐𝒙 BUT BEFORE WE DO LET’S….

Solve for x: 𝒙𝟐 − 𝟐𝒙 What are the solution(s) of y= 𝒙𝟐 − 𝟐𝒙

NOW GRAPH y= 𝒙𝟐 − 𝟐𝒙 a.) Find the x intercepts/ ROOTS/ZEROS


GRAPH y= 𝒙𝟐 − 𝟐𝒙 X intercept (s) Solution(s): Y intercept Vertex Axis of symmetry Domain Range


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10.) METHOD 2: FACTORING “WE DO” GRAPH y= 𝒙𝟐 − 𝟒𝒙

BUT BEFORE WE DO LET’S….

Solve for x: 𝒙𝟐 − 𝟒𝒙 What are the solution(s) of y= 𝒙𝟐 − 𝟒𝒙

NOW GRAPH y= 𝒙𝟐 − 𝟒𝒙 a.) Find the x intercepts/ ROOTS/ZEROS


GRAPH y= 𝒙𝟐 − 𝟒𝒙 X intercept (s) Solution(s): Y intercept Vertex Axis of symmetry Domain Range


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11.) METHOD 2: FACTORING “YOU DO” GRAPH y= 𝒙𝟐 − 𝟔𝒙

BUT BEFORE WE DO LET’S….

Solve for x: 𝒙𝟐 − 𝟔𝒙 What are the solution(s) of y= 𝒙𝟐 − 𝟔𝒙

NOW GRAPH y= 𝒙𝟐 − 𝟔𝒙 a.) Find the x intercepts/ ROOTS/ZEROS


GRAPH y= 𝒙𝟐 − 𝟔𝒙 X intercept (s) Solution(s): Y intercept Vertex Axis of symmetry Domain Range


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12.) METHOD 1….WHY?: “I DO” GRAPH y= −𝟑𝒙𝟐 BUT BEFORE WE DO LET’S….

Solve for x: −𝟑𝒙𝟐 What are the solution(s) of y= −𝟑𝒙𝟐

NOW GRAPH y= −𝟑𝒙𝟐

X intercept (s) Solution(s): Y intercept Vertex Axis of symmetry Domain Range

x y= −3𝑥! (x,y) -‐2

-‐1

0

1

2


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13.) “WE DO” GRAPH y= −𝟑𝒙𝟐 − 𝟔𝒙+ 𝟒


x y= −𝟑𝒙𝟐 − 𝟔𝒙+ 𝟒 (x,y) -‐3

-‐2

-‐1

0

1

2


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14.) “YOU DO” GRAPH y= 𝟐𝒙𝟐 − 𝟒𝑿− 𝟏


x y= 𝟐𝒙𝟐 − 𝟒𝑿− 𝟏 (x,y) -‐2

-‐1

0

1

2


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notes 1 solving and graphing quadratics and more - … 1 solvin… · ·...

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