Algebra 2 – Chapter 5.1 – 5.4 TestB
Name: ______________________________
Graph each function. State the axis of symmetry and the maximum or minimum value.
(6 points each)
1) y  3x 2  8
2) 𝑦 = −2𝑥 2 + 4𝑥 + 1
Axis of Symmetry: ___________
Axis of Symmetry: ___________
Max or Min (circle one) y-value is: _____
Max or Min (circle one) y-value is: _____
1
3) Identify the vertex and graph the function: y   ( x  1) 2  10 (6 points)
2
Vertex: _________
Determine whether the given function is linear or quadratic. Write your answer in the blank. Explain
your reasoning. (2 points)
4) f ( x)   x(5 x  8)
4) ______________
5) Identify the vertex and graph the function: y  2( x  5)2  6
(6 points)
Vertex: __________
6). Writing: Precisely describe the translation of the graph of 𝑦 = −3(𝑥 + 5)2 − 12 from the parent function
y  x 2 . Use correct vocabulary. (4 points)
Write the equation of the parabola in vertex form and then graph it. Show work.
(8 points)
7 𝑦 = 𝑥 2 − 4𝑥 + 1
Vertex form:____________________
Identify the vertex and the y-intercept of the graph of the function.
(2 points)
1
8) y   ( x  3) 2  11
3
8) Vertex: _________
y-intercept: _______
Write the function in standard form.
(3 points)
9) y  ( x  4) 2  10
9) ______________
Factor each expression.
(2 points each)
10) 20 x5  14 x 4  2 x3  12 x
11) 𝑥 2 − 9𝑥 − 36
10) ______________
11) ______________
12) x 2  x  12
13) 4𝑚2 − 20𝑚 + 25
12) ______________
13) ______________
14) 4 x 2  49
14) ______________
Factor each expression
(3 points each)
15)
1 2 1
n 
4
4
16) -3x2 +14x – 8
15) ______________
16) ______________
17) 2 x 2  3 x  20
18) 5𝑚2 − 1𝑚 − 4
17) ______________
18) ______________
19) A rock club’s profit from booking local bands depends on the ticket price. Using past receipts, the owners
find that the profit p can be modeled by the function p  15t 2  600t  50 where t represents the ticket price in
dollars. (6 points)
a) What price will give the maximum profit?
b) What is the maximum profit?