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Chapter 10: Q 341. (page 1240)

Graph the following parabolas by using intercepts, the vertex, and the axis of symmetry .

y=16x2+24x+9

Short Answer

Expert verified

The required graph is shown below:

Step by step solution

01

Given information

The given equation isy=16x2+24x+9

02

Determine the axis of symmetry.

By comparing the given equation with the standard form y=ax2+bx+cwe get a=16,b=24andc=9.

Since the value of a is positive so parabola opens up.

The axis of symmetry is the vertical line:

x=-b2a=-242(16)=-34

The axis of symmetry isx=-34.

03

Determine the vertex.

Put x=-34into the given equation we get.

y=16-342+24-34+9=9-18+9=0

The vertex is-34,0.

04

Determine the intercepts.

For y-intercept put x=0into the given equation.

y=16(0)2+24(0)+9y=9

The y-intercept is (0,9).

For x-intercept put y=0into the given equation.

role="math" localid="1653823101725" 0=16x2+24x+9(4x+3)2=0x=-34

The x-intercept is -34,0.

05

Draw the graph.

By using the above information the required graph is shown below:

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