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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 11: Q. 11.38TI (page 1100)

Find the equation of the parabolic arch formed in the foundation of the bridge shown. Write the equation in standard form.

Short Answer

Expert verified

The equation is $y = - \frac{1}{5} {(x - 5)}^{2} + 5$

Step by step solution

01

Given information

Given the base is $10 f t$ wide and $5 f t$ high

02

Calculate the vertex

Let the lower left side of the bridge be the origin of the coordinate grid at the point

Since the base is $10$ feet wide the point $(10, 0)$ represents the lower right side.

The bridge is $5$ feet high at the highest point. The highest point is the vertex of the parabola so the $y$ coordinate of the vertex will be $5$

So the vertex is $(5, 5)$

03

Step 3:Substitute in standard form and form the equation

Calculating, we get

$y = a (x - h)^{2} + k y = a {(x - 5)}^{2} + 5 0 = a {(0 - 5)}^{2} + 5 25 a = - 5 a = - \frac{1}{5}$

The equation is $y = - \frac{1}{5} {(x - 5)}^{2} + 5$

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Most popular questions from this chapter

For rational function, $f (x) = \frac{x - 1}{x^{2} - 6 x + 5}$ , a)find the domain of the function b) solve f(x) = 4c) find the points on the graph at this function value.

Multiply: $(a) (6 x + 5) (6 x - 5) (b) (4 p - 7 q) (4 p + 7 q)$

Use the Quotient Property to Simplify Radical Expressions

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

$a . \sqrt{\frac{72}{98}} b . \sqrt[3]{\frac{24}{81}} c . \sqrt[4]{\frac{6}{96}}$

Simplify each expression:

$ⓐ \frac{y^{43}}{y^{37}} ⓑ \frac{10^{15}}{10^{7}} ⓒ \frac{m^{7}}{m^{15}} ⓓ \frac{9^{8}}{9^{19}}$

Simplify each expression:

$ⓐ {(\frac{2}{3})}^{- 4} ⓑ {(- \frac{m}{n})}^{- 2}$

See all solutions

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