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Chapter 10: Q 318. (page 1238)

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

y=x2+8x+10

Short Answer

Expert verified

The given information is:

y=x2+8x+10

Step by step solution

01

Step 1. Given information.

The given information is:

y=x2+8x+10

02

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

y=ax2+bx+cy=x2+8x+10

The value of coefficient ais positive therefore we can say that the parabola opens up.

The axis of symmetry is the linex=-b2a.

Substitute the values of a, and binto the equation.

x=-821=-4

Therefore, the axis of symmetry is x=-4.

The vertex is on the line of symmetry, so its x-coordinate will be x=-4.

Now substitute the value ofxinto the equation,

y=-42+8-4+10=16-32+10=-6

Therefore, the vertex is-4,-6.

03

Step 3. Find the intercepts.

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

y=02+80+10=10

Therefore, the point 0,10 is the y-intercept.

We can see that the resultant point is left of the line of symmetry by 4 units.

Therefore the point right to the line of symmetry by 4 units is -8,10.


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

x2+8x+10=0x=-8卤82-411021x=-8卤242x=-4卤6

Therefore, the points of the x-intercept are-4+6,0and-4-6,0.

04

Step 4. Plot the graph.

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