Download Quadratic Formula Word Problems

NAME
4-6
DATE
PERIOD
Word Problem Practice
The Quadratic Formula and the Discriminant
1. PARABOLAS The graph of a quadratic
equation of the form y = ax2 + bx + c is
shown below.
4. EXAMPLES Give an example of a
quadratic function f (x) that has the
following properties.
I. The discriminant of f is zero.
y
II. There is no real solution of the
equation f(x) = 10.
5
Sketch the graph of x = f(x).
Sample answer: f (x) = -x 2
-5
O
x
O y
-4
2
Is the discriminant b - 4ac positive,
negative, or zero? Explain.
2
-2
4x
-2
Negative; the equation has no
real solutions so the
discriminant is negative.
-4
-6
-8
5. TANGENTS The graph of y = x2 is a
parabola that passes through the point
at (1, 1). The line y = mx - m + 1,
where m is a constant, also passes
through the point at (1, 1).
a. To find the points of intersection
between the line y = mx - m + 1
and the parabola y = x2, set x2 =
mx - m + 1 and then solve for x.
Rearranging terms, this equation
becomes x2 - mx + m - 1 = 0. What
is the discriminant of this equation?
No, b = -4 also works; the
x-axis will be tangent when the
discriminant b 2 - 16 is zero.
This happens when b = 4 or -4.
x2 - 4m + 4
3. SPORTS In 1990, American Randy
Barnes set the world record for the shot
put. His throw can be described by the
equation y = –16x2 + 368x. Use the
Quadratic Formula to find how far his
throw was to the nearest foot.
b. For what value of m is there only one
point of intersection? Explain the
meaning of this in terms of the
corresponding line and the parabola.
m = 2; the parabola y = x2 and
the line y = 2x - 1 have exactly
one point of intersection at
(1, 1). In other words, this line
is tangent to the parabola at
(1, 1).
23 ft
Chapter 4
40
Glencoe Algebra 2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
2. TANGENT Kathleen is trying to find b
so that the x-axis is tangent to the
parabola y = x2 + bx + 4. She finds one
value that works, b = 4. Is this the only
value that works? Explain.