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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 9: Q.487. (page 985)

Find $x$ and $y$ -intercepts.
$y = x^{2} + 16 x + 64$

Short Answer

Expert verified

The $x$ -intercepts is $(- 8, 0)$ .

The $y$ -intercepts is $(0, 64)$ .

Step by step solution

01

Step 1. Given information.

The given equation is $y = x^{2} + 16 x + 64$ .

02

Step 2. Determine the x-intercepts.

Substitute $y = 0$ in the given equation.

$\begin{array}{rcl} y & = & x^{2} + 16 x + 64 \\ x^{2} + 16 x + 64 & = & 0 \\ x^{2} + 8 x + 8 x + 64 & = & 0 \\ x (x + 8) + 8 (x + 8) & = & 0 \\ (x + 8) (x + 8) & = & 0 \\ 鈬� & x = - 8, - 8 \end{array}$

Hence, the required $x$ -intercepts is $(- 8, 0)$ .

03

Step 3. Determine the y-intercepts.

Substitute $x = 0$ in the given equation.

role="math" $\begin{array}{rcl} y & = & x^{2} + 16 x + 64 \\ = & 0^{2} + 16 脳 0 + 64 \\ = & 64 \end{array}$

Hence, the required $y$ -intercepts is $(0, 64)$ .

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