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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. 11.26 (page 1089)

a. Write $y = - 2 x^{2} + 8 x - 7$ in standard form.
b. use properties of standard form to graph the equation.

Short Answer

Expert verified

a. The standard form of the given equation is, $y = - 2 {(x - 2)}^{2} - 3$ .

b. The graph for the function $y = - 2 x^{2} + 8 x - 7$ is,

Step by step solution

01

Part a Step 1 Given equation is,

$y = - 2 x^{2} + 8 x - 7$ .

Rewrite the function in $y = a {(x - h)}^{2} + k$ form by completing the square.

role="math" localid="1645275386937" $y = - 2 (x^{2} - 4 x) - 7 y = - 2 (x^{2} - 4 x + 2) - 7 + 4 y = - 2 {(x - 2)}^{2} - 3$

02

Part b Step 1 Identify the constants a,h,k.

$a = - 2, h = 2, k = - 3$ .

Since $a = - 2$ , the parabola opens downward.

The axis of symmetry is, $x = h$ .

So, $x = 2$ .

The vertex is, $(h, k) = (2, - 3)$

Find the $y$ -intercept by substituting $x = 0$ in the given equation.

$y = 0 + 0 - 7 y = - 7$

The $y$ -intercept is, $(0, - 7)$ .

The point symmetric to $(0, - 7)$ across the axis of symmetry is, $(4, - 7)$ .

Find the $x$ - intercepts by substituting $y = 0$ in the given equation.

$0 = - 2 x^{2} + 8 x - 7$

Now factorize it.

$(x - 1.292) (x - 2.707) = 0 x = 1.292, 2.707$

The $x$ -intercepts are, $(1.292, 0), (2.707, 0)$ .

03

Step 2 Plot a graph for the given function with the known values.

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