Name:
Math 412
HW #
Date:
Quadratic Equations & Parabola
1)
Factor: 16 x 2  25 y 2
2) Solve:
4) The axes below are scaled by 1 unit. Using the
parabola graphed below, answer the questions that
follow.
5 x  13

x
6
a)
State the equation of the axis of symmetry.
b) State the vertex.
3) a) Graph the equation y  x 2  2 x  3 the set
of axes below.
c)
What are the roots/solutions to this parabola?
5) A contractor needs 54 square feet of brick to construct a
rectangular walkway. The length of the walkway is 15 feet
more than the width. Setup and solve an equation to find
the dimensions of the rectangle.
b) Clearly circle and state the roots of the equation
x2  2 x  3  0 .
6) What are the roots of the equation x2 − 7x + 6 = 0?
9) Factor: 4 x3  36 x
7) Find the vertex and axis of symmetry of the parabola
y = x2 − 16x + 63 without graphing.
10) Factor: 2x2 + 10x – 12
8) Use the parabola below to answer the question
that follows.
11) A rectangle has an area of 24 square
units. The width is 5 units less than the
length. What is the length, in units, of the
rectangle?
12) Does the parabola y = −x2 − 2x + 8
open upward or downward? Explain how
you know.
13) Solve: x2 − 6x = 0
14) Find three consecutive positive odd integers such that the product of the first and the second exceeds
the third by 8.
15) Which quadratic equation has 5 and – 4 as its solutions?
16) The quadratic expression 4 x 2  7 x  2 represents the area of a rectangular garden. What expressions
represent the dimensions of the garden?
17) A swim team member performs a dive from a 14-foot high springboard. The parabola below shows
the path of her dive.
18) Solve each equation for all values of x. Leave answers in simplest radical form, where necessary.
a)
x2  12 x  9  0
b) x 2  245