Unit 5 Recap ~ Part 1
Name
Find a quadratic model for the set of values.
1) (–1, 10), (2, 4), (3,–6)
2) A toy rocket is shot upward from ground level. The table shows the height of the rocket at different times.
a. Find a quadratic model for this data using your calculator.
b. Use the model to estimate the height of the rocket after 1.5 seconds.
3) The barber’s profit p each week depends on his charge c per haircut. It is modeled by the equation
p = – 200c2 + 2400c – 4700. What price should he charge for the largest profit?
Graph each function. Label the vertex, axis of symmetry, and y-intercept.
4) y = 2x –
1 2
x
4
6) y = –2x2 + 3
5) y = 2x2 + 12x + 8
Write the equation of the parabola in vertex form.
7)
8)
9)
5
5
5
4
4
4
3
3
3
2
2
2
1
1
-5 -4 -3 -2 -1
1
2
3
4
5
-5 -4 -3 -2 -1
1
1
2
3
4
5
-5 -4 -3 -2 -1
1
-1
-1
-1
-2
-2
-2
-3
-3
-3
-4
-4
-4
-5
-5
-5
2
3
4
5
Graph each function.
10) y  ( x  2)2  1
1
11) y  ( x  5)2  4
2
12) y  3( x 1)2  10
Write each function in vertex form.
13) y  x2  4 x  4
14) y  3x2  x  8
15) y  2 x2  6 x  10
Identify the vertex and y-intercept of the graph of each function.
16) y  4( x  5)2  1
17) y  2( x  5)2  3
Simplify each expression.
18)
48
19)
21)
16 + 2
22) (2 + 3i) + (–4 + 5i)
24) (2 + 3i)(4 + 5i)
300
25) (–1 + 4i)(1 – 2i)
20)
75
23) (5 + 14i) – (10 – 2i)