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Chapter 11: Q. 344 (page 1160)

Identify the type of graph of each equation as a circle, parabola, ellipse, or hyperbola b) write the equation in standard form and c) graph the equation.

y=x2+6x+8

Short Answer

Expert verified

The equation is parabola.

Step by step solution

01

Step 1. Given Information

Given that the equation isy=x2+6x+8.

02

Step 2. Form of the graph

Here, x and y are squared but not both called parabola. So, the equation is parabola. From the given equation,

a=1,b=6,c=8

When a=1, the parabola will open in the direction of upward.

The solution isy=x2+6x+8.

03

Step 3. Parameters

1) The parabola is opens in upward direction since the value of a is positive.

2) Axis of symmetry

x=-b2ax=-62脳1x=-3

The axis of symmetry is -3.

3) Vertex

y=(-3)2+6(-3)+8y=9-18+8y=-1Thevertexis(-3,-1).

4) y-intercept

whenx=0,y=(0)2+6(0)+8y=8y-interceptare(8,0)and(-4,2).

5) x-intercept

wheny=0,0=x2+6x+8x2+2x+4x+8x(x+2)+4(x+2)x=-4,-4

The x-intercepts are (-4,0) and (-2,0).

04

Step 4. Graph of the equation

On drawing the graph of the equation,

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