Name:
Math 412 – Parabola Review
HW #
Date:
4) Find the equation of the axis of symmetry for
1) The equation y = x + 3x – 18 is graphed below:
2
the parabola represented by y = 2 x2  3x  7
5) The area of the rectangular playground enclosure
at South School is 500 square meters. The length of
the playground is 5 meters longer than the width.
Find the dimensions of the playground, in meters.
a) State the roots of this parabola.
b) State the y-intercept.
2) Refer to the parabola below:
a) What is the equation of the axis of symmetry?
6) Which quadratic equation has – 6 as a solution?
7) If the area of a rectangle is represented by
x2 +8x +15 and the length is represented by
x + 5, what expression represents the width?
b) State the coordinates of the vertex.
8) Solve for x:
3) Find the vertex of the parabola represented by the
quadratic function f(x) = x2 – 16x + 63.
a) x2 = 16x – 28
b)
9) Factor: 5x3  20 x 2  60 x
14) Jane is 5 years older than Sally. If the product
of their ages is 75. Find their ages.
10)
a) On the set of axes below, graph y = x2 + 2x – 8.
b) Circle the roots of the parabola.
15) Solve: x2 – 5 = 5x – 5
16) Does the parabola y = –2x2 + 4x – 4 open
upward or downward? Explain how you know.
17) A ball is thrown in the air and its path is modeled by
the quadratic equation h = -16t2 + 30t + 6. If t = time, in
seconds, and h = the height the ball will reach, in feet,
find to the nearest tenth, the maximum height the ball
will reach.
11) Factor : 3x2 – 27
18) Which is the equation for the graph below?
12) When 24 is subtracted from the square of a
number, the result is five times the number.
What is the positive solution?
13) Find the roots of the equation.
y = 2x2 – 3x – 2.
19) In what 2 ways does the graph of f(x) = x2 differ
from g(x) = 3x2 + 2?