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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

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

01

Given information

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

02

Check whether the parabola is upward or downward

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

03

Find the axis of symmetry

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

On substituting the values we get

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

04

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 $(- \frac{5}{2}, - \frac{11}{2})$

05

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 $(- 5, 7)$

06

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 $(- 4.158, 0), (- 0.842, 0)$

07

plot the graph

The graph can be given as

08

Conclusion

The graph can be given as

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Most popular questions from this chapter

In the following exercises, use the Quotient Property to simplify square roots.

$\sqrt{\frac{108 y^{4}}{49}}$

Divide: $\frac{2 + 4 i}{5 i}$

In the following exercises, factor each trinomial of the form $x^{2} + b x + c$ .

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In the following exercises,simplify

$(a) \frac{r^{\frac{5}{2}} . r^{- \frac{1}{2}}}{r^{- \frac{3}{2}}} (b) (\frac{36 s^{\frac{1}{5}} t^{- \frac{3}{2}}}{s^{- \frac{9}{5}} . t^{\frac{1}{2}}})$

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