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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.481. (page 984)

Find (a) the equation of the axis of symmetry and (b) the vertex.
$y = 2 x^{2} - 8 x + 1$

Short Answer

Expert verified

Part (a). The equation of axis of symmetry is $x = 2$ .

Part (b). The vertex is $(2, - 7)$ .

Step by step solution

01

Part (a). Step 1. Given information.

The given equation is $y = 2 x^{2} - 8 x + 1$ .

02

Part (a). Step 2. Determine the equation of the axis of symmetry.

The axis of symmetry is given by $x = - \frac{b}{2 a}$ .

Compare the given equation $y = 2 x^{2} - 8 x + 1$ with $y = a x^{2} + b x + c$ .

So, here $a = 2, b = - 8, c = 1$ .

The required equation of the axis of symmetry is:

$\begin{array}{rcl} x & = & - \frac{b}{2 a} \\ = & - \frac{- 8}{2 脳 2} \\ = & \frac{8}{4} \\ = & 2 \end{array}$

03

Part (b). Step 1. Given information.

The given equation is $y = 2 x^{2} - 8 x + 1$ .

04

Part (b). Step 2. Determine the vertex.

Substitute $x = 2$ in the given equation $y = 2 x^{2} - 8 x + 1$ .

$\begin{array}{rcl} y (2) & = & 2 {(2)}^{2} - 8 脳 2 + 1 \\ = & 8 - 16 + 1 \\ = & - 8 + 1 \\ = & - 7 \end{array}$

Hence, the required vertex is $(2, - 7)$ .

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