Math  /  Algebra

QuestionQuestion 12 of 14, Step 1 of 2 14/20 Correct
Consider the function: f(x)=4x2+4x+9f(x)=4 x^{2}+4 x+9
Step 1 of 2 : Find the value of f(2)f(-2).
Answer f(2)=f(-2)= \square

Studdy Solution

STEP 1

What is this asking? We're given a function f(x)f(x) and we need to find its value when xx is 2-2. Watch out! Don't forget to follow the order of operations (PEMDAS/BODMAS) carefully, especially when squaring negative numbers!

STEP 2

1. Substitute the value
2. Calculate the result

STEP 3

Alright, let's **kick things off** by looking at our function: f(x)=4x2+4x+9f(x) = 4x^2 + 4x + 9.
We want to find f(2)f(-2), which means we need to **replace** every xx in the function with 2-2.
It's like substituting a player in a game!
So, let's do it!

STEP 4

When we **substitute** 2-2 for xx, we get: f(2)=4(2)2+4(2)+9f(-2) = 4 \cdot (-2)^2 + 4 \cdot (-2) + 9.
Notice how we've carefully replaced each xx with 2-2.

STEP 5

Now, let's **crank out the calculation**!
First, we deal with the exponent: (2)2=(2)(2)=4(-2)^2 = (-2) \cdot (-2) = 4.
Remember, a negative times a negative is a positive!
So, our expression becomes: f(2)=44+4(2)+9f(-2) = 4 \cdot 4 + 4 \cdot (-2) + 9.

STEP 6

Next, let's **tackle the multiplications**: 44=164 \cdot 4 = 16 and 4(2)=84 \cdot (-2) = -8.
Plugging these back in, we get: f(2)=16+(8)+9f(-2) = 16 + (-8) + 9.
Almost there!

STEP 7

Finally, let's **add everything up**: 16+(8)=816 + (-8) = 8, and then 8+9=178 + 9 = 17.
So, our **final result** is f(2)=17f(-2) = 17!
Boom!

STEP 8

f(2)=17f(-2) = 17

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