IXL - Match polynomials and graphs using zeros (Precalculus practice)

Match each polynomial function to its graph.

f
(
x
)
=
–
x
2
+
15
x
–
56
=
–
(
x
–
7
)
(
x
–
8
)
g
(
x
)
=
–
x
2
–
5

(

)

–

(

)

–

ref_doc_title.

Learn with an example

question

Match each polynomial function to its graph.

f
(
x
)
=
–
x
2
–
5
g
(
x
)
=
–
2
x
2
–
32
x
–
126
=
–
2
(
x
+
9
)
(
x
+
7
)

(

)

–

(

)

–

126

key idea

The graph of the quadratic function

is a parabola. If the leading coefficient is positive

(

the parabola opens up. If it is negative

(

the parabola opens down.

solution

First, classify each polynomial by its type.

Function	Type
f ( x ) = – x 2 – 5	Quadratic
g ( x ) = – 2 x 2 – 32 x – 126	Quadratic

The functions are both quadratic. To determine which function describes which graph, find the number of zeros for each.

Set

(

)

–

This function has no real zeros. That is, the function never intersects the

-axis.

Set

(

)

–

126

–

(

)

(

)

This function has two real zeros:

–

and

–

That is, the function intersects the

-axis

twice, at

–

and

–

To match

(

)

and

(

)

to their graphs, look at the places where the given graphs intersect the

-axis.

(

)

–

126

(

)

–

Looking for more? Try this:

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Teacher tools

Work it out

Not feeling ready yet? These can help:

D.4Match quadratic functions and graphs

F.1Find the roots of factored polynomials

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