Questions: 3.1 Homework Question 13, 3.1.29 HW Score: 50%, 11 of 22 points Part 2 of 4 Points: 0 of 1 Save For the function f(x)=x^2+x+5, complete parts (a)-(d) below. (a) Evaluate f(9). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. f(9)=95 (Simplify your answer.) B. f(9) is undefined. (b) Evaluate f(-5). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. f(-5)= (Simplify your answer.) B. f(-5) is undefined.

3.1 Homework
Question 13, 3.1.29
HW Score: 50%, 11 of 22 points
Part 2 of 4
Points: 0 of 1
Save

For the function f(x)=x^2+x+5, complete parts (a)-(d) below.
(a) Evaluate f(9). Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. f(9)=95 (Simplify your answer.)
B. f(9) is undefined.
(b) Evaluate f(-5). Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. f(-5)= (Simplify your answer.)
B. f(-5) is undefined.

Transcript text: 3.1 Homework Question 13, 3.1.29 HW Score: 50\%, 11 of 22 points Part 2 of 4 Points: 0 of 1 Save For the function $f(x)=\left|x^{2}+x+5\right|$, complete parts $(a)-(d)$ below. (a) Evaluate $f(9)$. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. $f(9)=95$ (Simplify your answer.) B. $f(9)$ is undefined. (b) Evaluate $f(-5)$. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. $f(-5)=\square$ (Simplify your answer.) $\square$ B. $f(-5)$ is undefined.

Solution

Solution Steps

Solution

Given the quadratic function $f(x) = |ax^2 + bx + c|$, where:

$a = 1$
$b = 1$
$c = 5$ And the value of $x$ is 9.

Step 1: Evaluate the Quadratic Expression

First, we calculate the quadratic expression $ax^2 + bx + c$ for the given value of $x$. Substituting the given values, we get $f(x) = 1(9)^2 + 1(9) + 5 = 95$.

Step 2: Apply Absolute Value

Then, we take the absolute value of the result obtained from step 1. Since the absolute value of any number is its non-negative value, $|f(x)| = |95| = 95$.

Final Answer:

The value of the function $f(x) = |ax^2 + bx + c|$ for $x = 9$ is ^95^.

Solution

Given the quadratic function $f(x) = |ax^2 + bx + c|$, where:

$a = 1$
$b = 1$
$c = 5$ And the value of $x$ is -5.

Step 1: Evaluate the Quadratic Expression

First, we calculate the quadratic expression $ax^2 + bx + c$ for the given value of $x$. Substituting the given values, we get $f(x) = 1(-5)^2 + 1(-5) + 5 = 25$.

Step 2: Apply Absolute Value

Then, we take the absolute value of the result obtained from step 1. Since the absolute value of any number is its non-negative value, $|f(x)| = |25| = 25$.

Final Answer:

The value of the function $f(x) = |ax^2 + bx + c|$ for $x = -5$ is ^25^.

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