Chapter 10: Q 315. (page 1238)

In the following exercises, graph by using intercepts, the vertex, and the axis of symmetry.
$y = x^{2} + 6 x + 13$

Short Answer

Expert verified

The given information is:

$y = x^{2} + 6 x + 13$

Step by step solution

Step 1. Given information.

The given information is:

$y = x^{2} + 6 x + 13$

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

$y = a x^{2} + b x + c y = x^{2} + 6 x + 13$

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

The axis of symmetry is the line $x = - \frac{b}{2 a}$ .

Substitute the values of a, and binto the equation.

$x = - \frac{6}{2 (1)} = - 3$

Therefore, the axis of symmetry is $x = - 3$ .

The vertex is on the line of symmetry, so its x-coordinate will be $x = - 3$ .

Now substitute the value of xinto the equation,

$y = {(- 3)}^{2} + 6 (- 3) + 13 = 9 - 18 + 13 = 4$

Therefore, the vertex is $(- 3, 4)$ .

Step 3. Find the intercepts.

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

$y = {(0)}^{2} + 6 (0) + 13 = 0 + 0 + 13 = 13$

Therefore, the point role="math" localid="1653843612331" $(0, 13)$ is the y-intercept.

We can see that the resultant point is right of the line of symmetry by 3 units.

Therefore the point left to the line of symmetry by 3 units is $(- 6, - 14)$ , it is symmetric to y-intercept.

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

$x^{2} + 6 x + 13 = 0 x = \frac{- 6 \pm \sqrt{6^{2} - 4 (1) (13)}}{2 (1)} x = \frac{- 6 \pm \sqrt{- 16}}{2}$

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

Step 4. Plot the graph.

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In the following exercises, graph by using intercepts, the vertex, and the axis of symmetry.
$y = x^{2} + 6 x + 13$

Short Answer

Step by step solution

Step 1. Given information.

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

Step 3. Find the intercepts.

Step 4. Plot the graph.

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In the following exercises, graph by using intercepts, the vertex, and the axis of symmetry.y=x2+6x+13

Short Answer

Step by step solution

Step 1. Given information.

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

Step 3. Find the intercepts.

Step 4. Plot the graph.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Decision Maths

Applied Mathematics

Statistics

Pure Maths

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

In the following exercises, graph by using intercepts, the vertex, and the axis of symmetry.
$y = x^{2} + 6 x + 13$