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