Chapter 11: Q.265 (page 1156)

In the following exercises, graph each equation by using its properties:
$y = 2 x^{2} + 10 x + 7$

Short Answer

Expert verified

The graph can be given as

Step by step solution

Given information

The equation of the parabola is $y = 2 x^{2} + 10 x + 7$

Check whether the parabola is upward or downward

As the value of coefficient of $x^{2}$ is positive the parabola is upward

Find the axis of symmetry

To find the axis of symmetry put $x = - \frac{b}{2 a}$

On substituting the values we get

$x = - \frac{10}{4} x = - \frac{5}{2}$

Find the vertex of the parabola

To find the vertex put $x = - \frac{5}{2}$ in the parabola equation

We get

$y = 2 x^{2} + 10 x + 7 y = 2 {(- \frac{5}{2})}^{2} + 10 (- \frac{5}{2}) + 7 y = \frac{25}{2} - \frac{50}{2} + 7 y = - \frac{11}{2}$

The vertex is at $(- \frac{5}{2}, - \frac{11}{2})$

To find the y-intercept put x=0

Put $x = 0$

We get

$y = 0 + 0 + 7 y = 7$

The coordinate of parabola is $(0, 7)$

As this coordinate is $\frac{5}{2} u n i t s$ to right of axis of symmetry the other coordinates is $\frac{5}{2} u n i t s$ left of the parabola.

Hence the coordinate is $(- 5, 7)$

Step 6; We write the x-intercept

To find the x-intercept we put $y = 0$

We get,

$2 x^{2} + 10 x + 7 = 0$

On solving we get

$x = - 4.158 a n d x = - 0.842$

The coordinates are $(- 4.158, 0), (- 0.842, 0)$

plot the graph

The graph can be given as

Conclusion

The graph can be given as

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In the following exercises, graph each equation by using its properties:
$y = 2 x^{2} + 10 x + 7$

Short Answer

Step by step solution

Given information

Check whether the parabola is upward or downward

Find the axis of symmetry

Find the vertex of the parabola

To find the y-intercept put x=0

Step 6; We write the x-intercept

plot the graph

Conclusion

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In the following exercises, graph each equation by using its properties:y=2x2+10x+7

Short Answer

Step by step solution

Given information

Check whether the parabola is upward or downward

Find the axis of symmetry

Find the vertex of the parabola

To find the y-intercept put x=0

Step 6; We write the x-intercept

plot the graph

Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Theoretical and Mathematical Physics

Statistics

Decision Maths

Logic and Functions

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

In the following exercises, graph each equation by using its properties:
$y = 2 x^{2} + 10 x + 7$