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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.271 (page 1156)

In the following exercise a) write the equation in standard form b) use properties of standard form to graph the parabola:
$y = - x^{2} + 12 x - 35$

Short Answer

Expert verified

The equation in standard form can be given as $y = - {(x - 6)}^{2} + 1$

The graph of the parabola can be given as

Step by step solution

01

Given information

We are given a equation $y = - x^{2} + 12 x - 35$

02

Write the equation in standard form

We have,

$y = - x^{2} + 12 x - 35 y = - 1 (x^{2} - 12 x) - 35 y = - 1 (x^{2} - 12 x + 36) + 36 - 35 y = - {(x - 6)}^{2} + 1$

03

Write the axis of symmetry and find the vertex of parabola

The axis of symmetry can be given as $x = h$

we get

The vertex of parabola isrole="math" localid="1645503068309" $(h, k) = (6, 1)$

04

Find y-intercept

Put $x = 0$

role="math" localid="1645503109752" $y = {- (0 - 6)}^{2} + 1 y = 36 + 1 y = 37$

The coordinate is $(0, 37)$

05

Find the point of symmetry (0,37)across the axis of symmetry

The point can be given as $(12, - 35)$

06

find the x-intercept

put $y = 0$

we get,

$- {(x - 6)}^{2} + 1 = 0 {(x - 6)}^{2} = 1 x - 6 = 卤 1 x = 5 o r x = 7$

07

Plot the graph of the parabola

The graph can be given as

08

Conclusion

The equation of the parabola can be given as $y = - {(x - 6)}^{2} + 1$

The graph can be given as

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Most popular questions from this chapter

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

$w^{2} + 10 x + 21$ .

Simplify each expression:

$鈸� \frac{y^{43}}{y^{37}} 鈸� \frac{10^{15}}{10^{7}} 鈸� \frac{m^{7}}{m^{15}} 鈸� \frac{9^{8}}{9^{19}}$

In the following exercises, multiply the rational expressions. $\frac{5 c^{2} + 9 c + 2}{c^{2} - 25} . \frac{c^{2} + 10 c + 25}{3 c^{2} - 14 c - 5}$

In the following exercises, simplify. $3 \sqrt{75 y^{2}} + 8 y \sqrt{48} - \sqrt{300 y^{2}}$

Simplify the rational expression $\frac{3 m^{2} + 30 m n + 75 n^{2}}{4 m^{2} - 100 n^{2}}$

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