Download Sample Questions – Quadratic Functions I F.IF.8

Sample Questions – Quadratic Functions I
F.IF.8
MULTIPLE CHOICE
1.
Use this description to write the quadratic function in vertex form:
The parent function
right and 5 units up.
is vertically stretched by a factor of 3 and translated 2 units
a.
b.
ANS: A
2.
Identify the vertex of
a. (
, )
b. (
, 8)
.
c.
d.
(14, )
(14, 8)
ANS: A
3.
Write the quadratic function c( x )  x 2  6 x  14 in vertex form.
a.
c.
b.
d.
ANS: A
4.
Write the quadratic function
in vertex form.
a.
c.
b.
d.
ANS: B
5.
Consider
. What are its vertex and y-intercept?
a. vertex: ( , 38), y-intercept: (0, 11)
c. vertex: ( , ), y-intercept: (0, 11)
b. vertex: (3, 2), y-intercept: (0, 11)
d. vertex: (0, 11), y-intercept: (3, 2)
ANS: B
6.
Consider
a. vertex: (
b. vertex: (
. What are its vertex and y-intercept?
, ), y-intercept:3
c. vertex: ( ,
, 3), y-intercept:
d. vertex: ( ,
), y-intercept: 3
), y-intercept:
ANS: C
7.
Consider the function
a.
b.
;
(2,
);
. Find its vertex and y-intercept.
c.
(2,
d.
(2, 0);
);
ANS: B
8.
Write
in vertex form.
a.
c.
b.
d.
ANS: A
9.
What is the minimum or maximum of
?
a.
minimum at
c.
minimum at (3, 0)
b.
maximum at
d.
maximum at (3, 0)
ANS: B
10.
What are the zeros of
a. 1, 5
b.
?
,1
c.
,
d.
,
ANS: B
11.
What are the zeros of the function
?
a.
,1
c.
,
b.
,1
d.
,2
ANS: A
12.
Find the zeros of
.
a.
and
c.
18 and
b.
and
d.
18 and
ANS: B
13.
Find the zeros of
.
a.
or
c.
or
b.
or
d.
or
ANS: D
14.
What is a quadratic function in standard form having zeros of
a.
c.
b.
d.
and
?
ANS: B
15.
What is a quadratic function in standard form having zeros of 5 and
a.
c.
b.
d.
?
ANS: C
SHORT ANSWER
1.
Use this description to write the quadratic function in vertex form:
The parent function
and 1 unit down.
is vertically stretched by a factor of 2 and translated 7 units right
ANS: f ( x)  2( x  7)2  1
2.
Identify the vertex of
.
ANS: V (11, 4)
3.
Identify the vertex of
.
ANS:
4.
Write the quadratic function c( x )  x 2  8x  12 in vertex form.
ANS: c( x )  ( x  4)2  4
5.
Write the quadratic function
in vertex form.
ANS:
6.
Find the zeros of
.
ANS: 5 and 
7.
The equation
gives the height h, in feet, of a baseball as a function of
time t, in seconds, after it is hit. How long does it take for the baseball to hit the ground?
5
2
ANS: about 2.6 s
ESSAY
1. Explain the zero-product property and why it is useful. Give an example to illustrate your
explanation.
ANS:
Sample answer: The zero-product property states that if a
product of factors is equal to zero, then one or more of the factors is equal to
zero. For example, in the equation x 2  4 x  12  0 the polynomial
x 2  4 x  12 can be factored as (x + 6)(x – 2). Since this factored
polynomial is equal to zero, then the value of at least one of the factors is 0.
This fact is useful because you can easily solve the equations x  6  0 and
x  2  0 to find the solutions x = –6 and x = 2.