Download Chapter 5 Review

Chapter 5 Review
1. y = -x2 + 6x – 5
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Direction ___________
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Axis of Symmetry: _________
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Vertex __________
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y-intercept __________
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x-intercept(s) __________
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symmetric point__________
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Maximum/Minimum__________
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Domain__________
 Range__________
2. y = 2x2 + 12x + 10

Direction ___________

Axis of Symmetry: _________

Vertex __________

y-intercept __________

x-intercept(s) __________

symmetric point__________

Maximum/Minimum__________

Domain__________
 Range__________
3) From 4 feet above a swimming pool, Susan throws a ball upward with a velocity of 32 feet per
second. The height, h(t), of the ball t seconds after Susan throws it is given by h(t) = -16t2 + v0t + h0.
a) Find the maximum height the ball reached.
b) When did the ball land in the pool?
4) Solve by factoring.
a) 6x2 – 2x = 0
b) x2 + x – 30 = 0
c) 2x2 – x – 3 = 0
d) 2x2 + 10 = 12x
e) x3 – 3x2 – 10x = 0
f) 3x2 – 13x – 10 = 0
5) Write a quadratic equation with the given roots.
a) 7 and 2
b)
1
and 2
3
c) -6 and 3
6) Complex Numbers.
Simplify.
a) i 64
e)
b) i 37
72
c) i 27
f)
48
d) i 46
g)
h) (7 + 2i) + (8 – 4i)
i) (9 + 6i) – (-13 + 10i)
k) (6 + 5i)(6 – 5i)
l)
24
81
j) (6 + 7i)(2 – 3i)
4  3i
6  5i
Solve.
m) 5x2 + 45 = 0
n) 7x2 + 84 = 0
Find the value of m and n to make each equation true.
o) (3m + 4) + (3 – n)i = 16 – 3i
p) (7 + n) + ( 4m – 10)i = 3 – 6i
7) Quadratic Formula and Discriminant
Find the discriminant for each quadratic equation and identify the number and type of roots.
a) x2 + 12x = -4
b) 2x2 – 7x – 4 = 0
c) 4x2 – 12x + 9 = 0
d) x2 + 2x + 6 = 0
Use the Quadratic Formula to solve each quadratic equation over the set of complex numbers.
a) 6x2 – 2x – 1 = 0
b) x2 + 64 = 16x
c) 3x2 + 8x – 3 = 0
d) 7x2 + 6x + 2 = 0
e) the height, h(t), in feet of an object t seconds after it is propelled straight up from the ground with
an initial velocity of 60 feet per second is modeled by the equation h(t) = -16t2 + 60t. At what time(s)
will the object be at a height of 56 feet?
8) Analyzing Graphs of Quadratic Equations
Write the quadratic equation in Vertex Form. Using the vertex and pattern of the parabola, quickly
graph the parabola.
a) y = x2 + 10x + 20
b) y = 2x2 + 12x + 18
c) y = x2 + 6x + 2
d) y = 2x2 – 4x –10
Write a quadratic equation for the parabola with the given vertex that passes through the given point.
e) vertex: (2, -3)
point: (4, 5)
f) vertex: (-4, 2)
point: (-2, 6)
g) vertex: (2, -6)
point: (5, 2)