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Chapter 13: Q. 2 (page 870)

Graph f(x)=x2+4x-5, by determining whether the graph opens up or down and by finding the vertex, axis of symmetry, and intercepts.

Short Answer

Expert verified

The graph of the function is:

Step by step solution

01

Step 1. Given information.

The function to be plotted is:

f(x)=x2+4x-5

The sign of x2is positive, so graph will open upward.

02

Step 2. To find x-intercept and y-intercept of the function.

The function can be written as:

y=x2+4x-5

y=x2+2.2x+22-22-5y=(x+2)2-4-5y=x+22-9

To find x-intercept:

(x+2)2-9=0(x+2)2-32=0(x+2-3)(x+2+3)=0(x-1)(x+5)=0x-1=0x=1x+5=0x=-5

x-intercepts are (1,0) and (-5,0)

To find y-intercept put x=0in the function.

localid="1647701094732" y=(0+2)2-9 y=4-9y=-5

y-intercept is (0,-5)

03

Step 3. To find vertex and axis of symmetry of the graph.

The equation of the parabola:

(x+2)2=(y+9)(x-(-2))=4.14(y-(-9))

By comparing the equation with standard form of parabola:(x-h)2=4a(y-k), where (h,k)is vertex of the parabola.

We get (h,k)=(-2,-9)

Vertex is: (-2,-9)

The axis of symmetry is:

localid="1647700708833" x+2=0x=-2

04

Step 4. To draw the graph of the function.

The graph of the given function can be drawn as:

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