Find the quadratic function f(x) = ax2 + bx + c for which f(-1) = 5, f(1) = 3, and f(2) = 5%3D

Name: Find the quadratic function f(x) = ax2 + bx + c for which f(-1) = 5,
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Description: Find the quadratic function f(x) = ax2 + bx + c for which f(-1) = 5, f(1) = 3, and f(2) = 5%3D

The given quadratic equation is fx=ax2+bx+c …1 and f-1=5, f1=3 and f2=5. Substitute…

Answered: Eind the quadratic function f/y) - oy2…

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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Find the quadratic function f(x) = ax2 + bx + c for which f(-1) = 5, f(1) = 3, and f(2) = 5
%3D

Expert Solution

Step 1

The given quadratic equation is $f (x) = a x^{2} + b x + c \dots (1)$

and $f (- 1) = 5$ , $f (1) = 3$ and $f (2) = 5$ .

Substitute $- 1$ , $1$ and $2$ in the given quadratic equation to obtain the values of $a$ , $b$ and $c$ .

Step 2

Substitute $- 1$ for $x$ in the quadratic equation $(1)$ .

$f (- 1) = a {(- 1)}^{2} + b (- 1) + c = a (1) - b + c = a - b + c$

But it is given that $f (- 1) = 5$ .

So, $a - b + c = 5 \dots (2)$

Substitute $1$ for $x$ in the quadratic equation $(1)$ .

$f (1) = a {(1)}^{2} + b (1) + c = a (1) + b + c = a + b + c$

But it is given that $f (1) = 3$ .

So, $a + b + c = 3 \dots (3)$

Substitute $2$ for $x$ in the quadratic equation $(1)$ .

$f (2) = a {(2)}^{2} + b (2) + c = a (4) + 2 b + c = 4 a + 2 b + c$

But it is given that $f (2) = 5$ .

So, $4 a + 2 b + c = 5 \dots (4)$

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