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)
Notes #1 Quadratics: “Graphing, Solving and more! Name:________________________
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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)
Notes #1 Quadratics: “Graphing, Solving and more! Name:________________________
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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
2
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Notes #1 Quadratics: “Graphing, Solving and more! Name:________________________
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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: ( , )
Notes #1 Quadratics: “Graphing, Solving and more! Name:________________________
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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
2
3
Notes #1 Quadratics: “Graphing, Solving and more! Name:________________________
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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
Notes #1 Quadratics: “Graphing, Solving and more! Name:________________________
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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 ?
Notes #1 Quadratics: “Graphing, Solving and more! Name:________________________
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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
Notes #1 Quadratics: “Graphing, Solving and more! Name:________________________
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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
Notes #1 Quadratics: “Graphing, Solving and more! Name:________________________
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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
b.) Find the y intercept of c.) Find the VERTEX
GRAPH y= 𝒙𝟐 − 𝟒 X intercept (s) Solution(s): Y intercept Vertex Axis of symmetry Domain Range
Notes #1 Quadratics: “Graphing, Solving and more! Name:________________________
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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
b.) Find the y intercept of c.) Find the VERTEX
GRAPH y= 𝟗𝒙𝟐 − 𝟏𝟔 X intercept (s) Solution(s): Y intercept Vertex Axis of symmetry Domain Range
Notes #1 Quadratics: “Graphing, Solving and more! Name:________________________
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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
b.) Find the y intercept of c.) Find the VERTEX
GRAPH y= 𝒙𝟐 − 𝟐𝒙 X intercept (s) Solution(s): Y intercept Vertex Axis of symmetry Domain Range
Notes #1 Quadratics: “Graphing, Solving and more! Name:________________________
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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
b.) Find the y intercept of c.) Find the VERTEX
GRAPH y= 𝒙𝟐 − 𝟒𝒙 X intercept (s) Solution(s): Y intercept Vertex Axis of symmetry Domain Range
Notes #1 Quadratics: “Graphing, Solving and more! Name:________________________
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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
b.) Find the y intercept of c.) Find the VERTEX
GRAPH y= 𝒙𝟐 − 𝟔𝒙 X intercept (s) Solution(s): Y intercept Vertex Axis of symmetry Domain Range
Notes #1 Quadratics: “Graphing, Solving and more! Name:________________________
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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
Notes #1 Quadratics: “Graphing, Solving and more! Name:________________________
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13.) “WE DO” GRAPH y= −𝟑𝒙𝟐 − 𝟔𝒙+ 𝟒
X intercept (s) Solution(s): Y intercept Vertex Axis of symmetry Domain Range
x y= −𝟑𝒙𝟐 − 𝟔𝒙+ 𝟒 (x,y) -‐3
-‐2
-‐1
0
1
2
Notes #1 Quadratics: “Graphing, Solving and more! Name:________________________
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14.) “YOU DO” GRAPH y= 𝟐𝒙𝟐 − 𝟒𝑿− 𝟏
X intercept (s) Solution(s): Y intercept Vertex Axis of symmetry Domain Range
x y= 𝟐𝒙𝟐 − 𝟒𝑿− 𝟏 (x,y) -‐2
-‐1
0
1
2
Notes #1 Quadratics: “Graphing, Solving and more! Name:________________________
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Notes #1 Quadratics: “Graphing, Solving and more! Name:________________________
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Notes #1 Quadratics: “Graphing, Solving and more! Name:________________________
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Notes #1 Quadratics: “Graphing, Solving and more! Name:________________________
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Notes #1 Quadratics: “Graphing, Solving and more! Name:________________________
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Notes #1 Quadratics: “Graphing, Solving and more! Name:________________________
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Notes #1 Quadratics: “Graphing, Solving and more! Name:________________________
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Notes #1 Quadratics: “Graphing, Solving and more! Name:________________________
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Notes #1 Quadratics: “Graphing, Solving and more! Name:________________________
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