Identify the quadratic function from the graph-2-4-3-2-124a) f(x) = x² – 4x + 5b) f(x) = x² – 2x + 3c) f(x) = x² + 4x + 5d) f(x) = x² + 2x + 3Select one:O (d)(b)(c)(a)

Answered: Identify the quadratic function from…

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter3: Polynomial And Rational Functions

Section3.1: Quadratic Functions And Models

Problem 1E: To put the quadratic function f(x)=ax2+bx+c in standard form, we complete the ________________.

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Question

Identify the quadratic function from the graph
-2
-4
-3
-2
-1
2
4
a) f(x) = x² – 4x + 5
b) f(x) = x² – 2x + 3
c) f(x) = x² + 4x + 5
d) f(x) = x² + 2x + 3
Select one:
O (d)
(b)
(c)
(a)

Expert Solution

Step 1

Consider the quadratic equation given in part (a),

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

from the graph, it can be observed that the y-intercept of the graph is $(0, 3)$ .

so, check that the point $(0, 3)$ will satisfy the equation or not,

$3 \overset{?}{=} {(0)}^{2} - 4 (0) + 5 3 \neq 5$

since the point does not satisfy the equation so, the given function does not represent the graph.

Consider the quadratic equation given in part (b),

$f (x) = x^{2} - 2 x + 3$

from the graph, it can be observed that the y-intercept of the graph is $(0, 3)$ .

so, check that the point $(0, 3)$ will satisfy the equation or not,

$3 \overset{?}{=} {(0)}^{2} - 2 (0) + 3 3 = 3$

also, from the graph the vertex of the function is $(- 1, 2)$

so, check that the point $(- 1, 2)$ will satisfy the equation or not,

$2 \overset{?}{=} {(- 1)}^{2} - 2 (- 1) + 3 2 \overset{?}{=} 1 + 2 + 3 2 \neq 6$

Since, the point does not satisfy the equation so, the given function does not represent the graph.

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Identify the quadratic function from the graph -2 -4 -3 -2 -1 2 4 a) f(x) = x² – 4x + 5 b) f(x) = x² – 2x + 3 c) f(x) = x² + 4x + 5 d) f(x) = x² + 2x + 3 Select one: O (d) (b) (c) (a)