Name:_________________________________________ Period:__________

SM2 Unit 6A Quadratic Graphs Test Review

SM 2

Circle the equation that best describes each graph. 1. 2. 3. A. ( )( )1

2 4 2y x x= + − A. ( )23 4 6y x= − − − A. ( ) 2 8 15f x x x= + +

B. ( )( )2 4 2y x x= + − B. ( )23 4 6y x= − + − B. ( ) 2 8 15f x x x= − +

C. ( )( )2 4 2y x x= − + C. ( )23 4 6y x= − + + C. ( ) 2 4 1f x x x= + −

D. ( )( )12 4 2y x x= − + D. ( )23 4 6y x= − − + D. ( ) 2 4 1f x x x= − −

Fill in the requested information. Then graph the function. Plot at least five points! Show work if needed! 4. ( ) ( )22 3f x x= + − 𝑎 = ________ ℎ = ________ 𝑘 = _________ Vertex:____________________ Is the vertex a maximum or a minimum? __________ Axis of Symmetry:__________________ Direction of Opening:________________ Show work here:

𝒙 𝒇(𝒙)

Vertex

5. ( )21 1 42

y x= − − +

𝑎 = ________ ℎ = ________ 𝑘 = _________ Vertex:____________________ Is the vertex a maximum or a minimum? __________ Axis of Symmetry:__________________ Direction of Opening:________________ Show work here: 6. ( ) 2 8 10f x x x= − + − 𝑎 = ________ 𝑏 = ________ 𝑐 = _________ Vertex:____________________ Is the vertex a maximum or a minimum? __________ Axis of Symmetry:__________________ Direction of Opening:________________ Show work here:

𝒙 𝒚

Vertex

𝒙 𝒇(𝒙)

Vertex

7. 22 4 3y x x= − − 𝑎 = ________ 𝑏 = ________ 𝑐 = _________ Vertex:____________________ Is the vertex a maximum or a minimum? __________ Axis of Symmetry:__________________ Direction of Opening:________________ Show work here: For each function, do the following: 1) state whether the function is in standard, vertex, or factored form, 2) find the zeros (real and imaginary), 3) find the y-intercept. Show work! 8. ( ) 25 25f x x x= + 9. ( )( )3 7 4y x x= − − + Form:____________________ Form:____________________ Zero(s): _________________________ Zero(s): _________________________ 𝑥-intercept: __________________ 𝑥-intercept: __________________ 𝑦-intercept: __________________ 𝑦-intercept: __________________ Show work here: Show work here:

𝒙 𝒚

Vertex

10. ( ) 2 7 10f x x x= + + 11. ( ) ( )23 16f x x= − − Form:____________________ Form:____________________ Zero(s): _________________________ Zero(s): _________________________ 𝑥-intercept: __________________ 𝑥-intercept: __________________ 𝑦-intercept: __________________ 𝑦-intercept: __________________ Show work here: Show work here: 12. ( ) ( )25 11f x x= − − − 13. ( )2 3y x x= − − Form:____________________ Form:____________________ Zero(s): _________________________ Zero(s): _________________________ 𝑥-intercept: __________________ 𝑥-intercept: __________________ 𝑦-intercept: __________________ 𝑦-intercept: __________________ Show work here: Show work here:

Vocabulary

Write the letter of the definition that best describes each word, phrase, or expression in the appropriate blank. One of the definitions will be used three times! _____ Axis of Symmetry (What is it?) _____ Equation of the Axis of Symmetry _____ Factored Form of a Quadratic Function _____ Maximum Point _____ Minimum Point

_____ 2

ba−

_____ Quadratic Function _____ Roots _____ Standard Form of a Quadratic Function _____ Vertex _____ Vertex Form of a Quadratic Function _____ x-Intercepts _____ Zeros

A. ( ) 2 , where 0.f x ax bx c a= + + ≠ B. The vertex of a parabola that opens upward

is the ________ of the graph. C. The vertical line that divides a parabola in

half. D. ( ) ( )2 , where 0.f x a x h k a= − + ≠ E. The vertex of a parabola that opens

downward is the ________ of the graph. F. The set of x–values which make ( ) 0,f x =

indicating where the graph will cross the x-axis.

G. ( ) ( )( ) , where 0.f x a x p x q a= − − ≠ H. The point where the parabola changes

direction – the “tip” of the parabola. ( ),h k

from the equation ( ) ( )2 ,f x a x h k= − + where 0.a ≠

I. 2

bxa−

= for a quadratic function in standard

form or x h= for a quadratic function in vertex form.

J. The type of function whose graph is a

parabola. It can be written in standard form, vertex form, or factored form.

K. This expression gives the x-coordinate of the

vertex of a parabola when the equation is written in standard form.