Name: ________________________________________________
Date: ______________
ALEGBRA I UNITS 6 & 7 ASSESSMENT
_______ 1. Write 8x2 – 5 + 7x4 – 9x – x5 in standard form.
A
B
C
D
−9x + 8x2 + 7x4 – 5 – x5
8x2 – 5 + 7x4 – 9x – x5
−x5 + 7x4 + 8x2 – 9x − 5
−5 – 9x + 8x2 + 7x4 – x5
_______ 2. Find the product. −8y2(2y2 + 7y – 5)
A
B
C
D
−16y4 – 56y – 40
−16y4 – 56y3 + 40y2
16y4 + 56y3 – 40y2
−6y4 – y3 – 13y2
_______ 3. What is the prime factorization of 84?
A
B
C
D
2∙3∙7
3∙4∙7
2 ∙ 2 ∙ 21
2∙2∙3∙7
_______ 4. Factor out the greatest common factor from the terms of the polynomial
2x3 – 5x2 + 25.
A
B
C
D
x2(2x – 5) + 25
The expression is already fully
factored.
5x(x2 – x + 5)
2x3 – 5(x2 – 5)
ALEGBRA I UNITS 6 & 7 ASSESSMENT P. 1
Name: ________________________________________________
Date: ______________
_______ 5. What is the factored form of x2 + 3xy – 10y2?
(x + 2y)(x – 5y)
(x – 2y)(x + 5y)
x(x + 3y) – y(3x – 10y)
The expression is already fully
factored.
A
B
C
D
_______ 6. Factor the perfect square trinomial x2 – 12x + 36.
(x – 6)2
(x – 6)(x + 6)
(x + 6)2
(x – 12)2
A
B
C
D
_______ 7. The graph of g(x) = ax2 opens downward and is narrower than the graph of
f(x) = x 2. Which of the following could be the value of a?
a)
b)
c)
d)
−3
−0.6
0.5
2
_______ 8. What is the average rate of change of the function f(x) = 2x2 + x + 5 over the
interval −2 ≤ x ≤ 2?
A −4
B −1
C1
D 4
ALEGBRA I UNITS 6 & 7 ASSESSMENT P. 2
Name: ________________________________________________
Date: ______________
_______ 9. What is the axis of symmetry for the function y = −(x − 3)2 + 5?
a) x = −5
b) x = −3
c) x = 3
d) x = 5
_______ 10. Which of the following functions has a graph with a vertex that is a
translation 5 units horizontally to the right of the vertex of the graph of
g(x)= (x + 2)2 + 2?
a) g(x) = −(x − 3)2 + 2
b) g(x) = (x + 7) 2 + 2
c) g(x) = (x + 5)2 + 2
d) g(x) = −(x + 2)2 + 5
_______ 11. The function h(t) = −16t 2 + 24t models the height, in feet, of a kangaroo t seconds
after it jumps. What is the maximum height of the jump?
a)
b)
c)
d)
9 ft
18 ft
27 ft
36 ft
.
ALEGBRA I UNITS 6 & 7 ASSESSMENT P. 3
Name: ________________________________________________
Date: ______________
_______ 12. Which function best models the data?
a) h(t) = −15.9t 2 + 2.99t +10.22
b) h(t) = −16.1t 2 + 10.22t + 2.99
c) h(t) = −5.03t 2 + 10.22t + 2.99
d) h(t) = −5.03t 2 + 2.99t + 10.22
_______ 13. Over what interval does f(x) = 3xincrease faster than g(x) = 9x?
a)
b)
c)
d)
0 < x<3
x>3
0<x<2
2 <x <3
_______ 14. Which of the following expressions(s) are fourth-degree trinomials? Select all that
apply.
a)
b)
c)
d)
3x2y + 5x3y + 6y4
6y4 + 5x3 + 1
5xy – 5x2y2 + 7
3y3 + 3x3y3
1
_______ 15. Which statements about the graphs of functions 𝑔(𝑥) = − 𝑥 2 and 𝑓(𝑥) = 𝑥 2
4
true? Select all that apply.
a) g is wider than f
b) f and g open in the same direction
c) f and g have the same vertex
d) f and g have the same axis of symmetry
ALEGBRA I UNITS 6 & 7 ASSESSMENT P. 4
Name: ________________________________________________
Date: ______________
16. Simplify: (5x3 + 7x – 8) + (2x3 – 5x2 – x + 3). Write your answer in standard form.
17. Find the product. (6x2 + 8)(3x2 – 5x + 7)
18. A portrait without its frame has a height 1.5 times its width w, in inches. Its frame is 2 in.
wide all along its perimeter. What is an expression for the area of the framed portrait in terms of
w? Simplify your expression and write it in standard form.
19. What is the greatest common factor of the terms of the polynomial –16y4 + 12y2 – 4y?
20. Factor the perfect square trinomial 16y2 – 24y + 9.
ALEGBRA I UNITS 6 & 7 ASSESSMENT P. 5
Name: ________________________________________________
Date: ______________
21. Identify the vertex and y-intercept of the graph of the function y = (x + 2)2 − 3.
vertex:
y-intercept:
22. The graph of h is a translation 4 units right and 1 unit down of the graph of
f(x) = x 2. Write function h in vertex form.
23. The rate of change of function f is the same from x = −2 to x = 1 as it is from x = 1 to x = 4. Is
function f linear, quadratic, or exponential?
24. The function f(x) = −4x2 + 18x + 16 models the predicted sales of a hat after x price
increases. Use the table showing actual and predicted sales to find the residuals for the model.
ALEGBRA I UNITS 6 & 7 ASSESSMENT P. 6
Name: ________________________________________________
Date: ______________
Performance Assessment
25. A high school drama club is selling tickets for a
fundraiser event. Based on data from past events, the
number of tickets sold can be modeled by a linear function
Q(x) = −40x + 640, where x is the price, in dollars, of each
ticket.
Part A
What is a reasonable domain and range for function Q?
Explain.
Part B
The revenue R can be determined by multiplying the ticket price x by the number of tickets
sold. Write a quadratic function R that correctly represents this model. Justify your answer.
Part C
Graph function R below. Label the vertex. What does the vertex represent in this context?
Explain.
ALEGBRA I UNITS 6 & 7 ASSESSMENT P. 7