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Chapter 10: Q 316. (page 1238)

In the following exercises, graph by using intercepts, the vertex, and the axis of symmetry.

y=-2x2-8x-12

Short Answer

Expert verified

The given information is:

y=-2x2-8x-12

Step by step solution

01

Step 1. Given information.

The given information is:

y=-2x2-8x-12

02

Step 2. Find the axis of symmetry and the vertex.

y=ax2+bx+cy=-2x2-8x-12

The value of coefficient ais negative therefore we can say that the parabola opens down.

The axis of symmetry is the linex=-b2a.

Substitute the values of a, and binto the equation.

x=--82-2=-2

Therefore, the axis of symmetry is x=-2.

The vertex is on the line of symmetry, so its x-coordinate will be x=-2.

Now substitute the value of xinto the equation,

y=2-22-8-2-12=24+16-12=-8+4=-4

Therefore, the vertex is-2,-4.

03

Step 3. Find the intercepts.

Now substitute xequal to 0 in the equation to find the intercept y,

y=-202-80-12=-0-0-1=-12

Therefore, the point 0,-12 is the y-intercept.

We can see that the resultant point is right of the line of symmetry by 2 units.

Therefore the point right to the line of symmetry by 2 units is -4,-12.


Now substitute yequal to 0 in the equation to find the intercept x,

-2x2-8x-12=0x=--8卤-82-4-2-122-2x=8卤-36-4

There is no x-intercept because a square root is not possible for a negative number.

04

Step 4. Plot the graph.

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