Chapter 9 Algebra Worksheet With Answers - Montville Township Public Schools
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31Study Guide and Review - Chapter 9
State whether each sentence is true or false . If false , replace the underlined term to make a true
sentence.
1. The axis of symmetry of a quadratic function can be found by using the equation x =
.
SOLUTION:
The shape of the graph of a quadratic function is called a parabola. Parabolas are symmetric about a central line
called the axis of symmetry. The axis of symmetry of a quadratic function can be found by using the equation
. The statement is true.
2. The vertex is the maximum or minimum point of a parabola.
SOLUTION:
The axis of symmetry intersects a parabola at only one point, called the vertex. The lowest point on the graph is the
minimum, and the highest point on the graph is the maximum. The vertex is the maximum or minimum point of a
parabola. The statement is true.
3. The graph of a quadratic function is a straight line.
SOLUTION:
2
Quadratic functions are nonlinear and can be written in the form f (x) = ax
+ bx + c, where a ≠ 0. So, the statement
is false. The graph of a quadratic function is a parabola .
2
4. The graph of a quadratic function has a maximum if the coefficient of the x
-term is positive.
SOLUTION:
2
When a > 0, the graph of y = ax
+ bx + c opens upward. The lowest point on the graph is the minimum. So, the
2
statement is false. The graph of a quadratic function has a minimum if the coefficient of the x
-term is positive.
5. A quadratic equation with a graph that has two x-intercepts has one real root.
SOLUTION:
The solutions or roots of a quadratic equation can be identified by finding the x-intercepts of the related graph. So,
the statement is false. A quadratic equation with a graph that has two x-intercepts has two real roots.
2
6. The expression b
− 4ac is called the discriminant.
SOLUTION:
2
In the Quadratic Formula, the expression under the radical sign, b
− 4ac, is called the discriminant. The statement is
true.
7. The solutions of a quadratic equation are called roots.
SOLUTION:
The solutions of a quadratic equation are called roots. The statement is true.
2
8. The graph of the parent function is translated down to form the graph of f (x) = x
+ 5.
SOLUTION:
2
If c > 0 in f (x) = x
+ c, the graph of the parent function is translated
units up. So, the statement is false. The
2
graph of the parent function is translated up 5 units to form the graph of f (x) = x
+ 5.
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State whether each sentence is true or false . If false , replace the underlined term to make a true
sentence.
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