Q. 5 In Problems 4 and 5,(a) Determin... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 3: Q. 5 (page 175)

In Problems 4 and 5,
(a) Determine whether the graph opens up or down.
(b) Determine the vertex of the graph of the quadratic function.
(c) Determine the axis of symmetry of the graph of the quadratic
function.
(d) Determine the intercepts of the graph of the quadratic function.
(e) Use the information in parts (a)鈥�(d) to graph the quadratic
function.
(f) Based on the graph, determine the domain and the range of
the quadratic function.
(g) Based on the graph, determine where the function is
increasing and where it is decreasing.
$g (x) = - 2 x^{2} + 4 x - 5$

Short Answer

Expert verified

(a) Graph is open down.

(b) Vertex $= (1, - 3)$

(d) y-intercept $(0, - 5)$ . No x-intercept.

(f) Domain $= (- 鈭�, 鈭�)$ and Range $= (- 鈭�, - 3]$

(g) The function is decreasing in $[1, 鈭�)$ and increasing in .

(e)

Step by step solution

Part (a) Step 1. Given Information

$g (x) = - 2 x^{2} + 4 x - 5$

Part (a) Step 2. Calculation

Comparing the given function with $f (x) = a x^{2} + b x + c$ we get,

$a = - 2, b = 4 & c = - 5$

Hence $a < 0$ then the graph is open down.

Part (b) Step 1. Given Information

$g (x) = - 2 x^{2} + 4 x - 5$

Part (b) Step 2. Calculation

Since $g (x) = - 2 x^{2} + 4 x - 5$

$= - 2 {(x - 1)}^{2} - 3$

Therefore vertex is at $(1, - 3)$

Part (c) Step 1. Given Information

$g (x) = - 2 x^{2} + 4 x - 5$

Part (c) Step 2. Calculation

Since vertex is at $(1, - 3)$

The graph of the function is symmetric about $x = 1$

Part (d) Step 1. Given Information

$g (x) = - 2 x^{2} + 4 x - 5$

Part (d) Step 2. Calculation

For y-intercept $x = 0$ ,

Then $f (0) = - 2.0 + 4.0 - 5$

$= - 5$

Therefore y-intercept is $(0, - 5)$

For x-intercept, $16 - 4 . (- 2) . (- 5) < 0$

Hence there is no x-intercept.

Part (e) Step 1. Given Information

$g (x) = - 2 x^{2} + 4 x - 5$

Part (e) Step 2. Graph

Part (f) Step 1. Given Information

$g (x) = - 2 x^{2} + 4 x - 5$

Part (f) Step 2. Calculation

The domain of the given function is $(- 鈭�, 鈭�)$ .

The range of the function is $(- 鈭�, - 3]$

Part (g) Step 1. Given Information

$g (x) = - 2 x^{2} + 4 x - 5$

Part (g) Step 2. Calculation

By the graph, the function is increasing in the interval $(- 鈭�, 1]$ and the function is decreasing in the interval $[1, 鈭�)$ .

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91影视

Short Answer

Step by step solution

Part (a) Step 1. Given Information

Part (a) Step 2. Calculation

Part (b) Step 1. Given Information

Part (b) Step 2. Calculation

Part (c) Step 1. Given Information

Part (c) Step 2. Calculation

Part (d) Step 1. Given Information

Part (d) Step 2. Calculation

Part (e) Step 1. Given Information

Part (e) Step 2. Graph

Part (f) Step 1. Given Information

Part (f) Step 2. Calculation

Part (g) Step 1. Given Information

Part (g) Step 2. Calculation

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