Math / Algebra

QuestionGiven the function $f(x)=-3 x^{2}+8$ , calculate the following values. If the answer is undefined, write DNE. $f(8)=$ $\square$ $f(-6)=$ $\square$ $f(0)=$ $\square$

Studdy Solution

STEP 1

What is this asking? We're given a function $f(x)$ and we need to find its value at a few different x values. Watch out! Make sure to follow the order of operations (PEMDAS/BODMAS) carefully, especially when squaring negative numbers!
Also, remember that $f(8)$ means we substitute $8$ for x in the function $f(x)$ .

STEP 2

1. Calculate $f(8)$
2. Calculate $f(-6)$
3. Calculate $f(0)$

STEP 3

Let's substitute $x = 8$ into our function $f(x) = -3x^2 + 8$ .
This gives us $f(8) = -3 \cdot (8)^2 + 8$ .

STEP 4

First, we square the $\textbf{8}$ : $(8)^2 = 64$ .
So, $f(8) = -3 \cdot 64 + 8$ .

STEP 5

Next, we multiply $-3$ by $64$ : $-3 \cdot 64 = -192$ .
So, $f(8) = -192 + 8$ .

STEP 6

Finally, we add $-192$ and $8$ : $-192 + 8 = -184$ .
So, $f(8) = \textbf{-184}$ .

STEP 7

Now, let's substitute $x = -6$ into our function: $f(-6) = -3 \cdot (-6)^2 + 8$ .

STEP 8

We square $-6$ : $(-6)^2 = 36$ .
Remember, a negative times a negative is a positive!
So, $f(-6) = -3 \cdot 36 + 8$ .

STEP 9

Next, we multiply $-3$ by $36$ : $-3 \cdot 36 = -108$ .
So, $f(-6) = -108 + 8$ .

STEP 10

Finally, we add $-108$ and $8$ : $-108 + 8 = -100$ .
So, $f(-6) = \textbf{-100}$ .

STEP 11

Let's substitute $x = 0$ into our function: $f(0) = -3 \cdot (0)^2 + 8$ .

STEP 12

Anything multiplied by zero is zero, so $-3 \cdot (0)^2 = -3 \cdot 0 = 0$ .
This simplifies our equation to $f(0) = 0 + 8$ .

STEP 13

Adding zero to any number doesn't change the number, so $0 + 8 = 8$ .
Therefore, $f(0) = \textbf{8}$ .

STEP 14

$f(8) = -184$ $f(-6) = -100$ $f(0) = 8$

Was this helpful?

QuestionGiven the function $f(x)=-3 x^{2}+8$ , calculate the following values. If the answer is undefined, write DNE. $f(8)=$ $\square$ $f(-6)=$ $\square$ $f(0)=$ $\square$

Studdy Solution

STEP 1

STEP 2

1. Calculate $f(8)$
2. Calculate $f(-6)$
3. Calculate $f(0)$

STEP 3

Let's substitute $x = 8$ into our function $f(x) = -3x^2 + 8$ .
This gives us $f(8) = -3 \cdot (8)^2 + 8$ .

STEP 4

First, we square the $\textbf{8}$ : $(8)^2 = 64$ .
So, $f(8) = -3 \cdot 64 + 8$ .

STEP 5

Next, we multiply $-3$ by $64$ : $-3 \cdot 64 = -192$ .
So, $f(8) = -192 + 8$ .

STEP 6

Finally, we add $-192$ and $8$ : $-192 + 8 = -184$ .
So, $f(8) = \textbf{-184}$ .

STEP 7

Now, let's substitute $x = -6$ into our function: $f(-6) = -3 \cdot (-6)^2 + 8$ .

STEP 8

We square $-6$ : $(-6)^2 = 36$ .
Remember, a negative times a negative is a positive!
So, $f(-6) = -3 \cdot 36 + 8$ .

STEP 9

Next, we multiply $-3$ by $36$ : $-3 \cdot 36 = -108$ .
So, $f(-6) = -108 + 8$ .

STEP 10

Finally, we add $-108$ and $8$ : $-108 + 8 = -100$ .
So, $f(-6) = \textbf{-100}$ .

STEP 11

Let's substitute $x = 0$ into our function: $f(0) = -3 \cdot (0)^2 + 8$ .

STEP 12

Anything multiplied by zero is zero, so $-3 \cdot (0)^2 = -3 \cdot 0 = 0$ .
This simplifies our equation to $f(0) = 0 + 8$ .

STEP 13

Adding zero to any number doesn't change the number, so $0 + 8 = 8$ .
Therefore, $f(0) = \textbf{8}$ .

STEP 14

$f(8) = -184$ $f(-6) = -100$ $f(0) = 8$

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionGiven the function f(x)=−3x2+8f(x)=-3 x^{2}+8f(x)=−3x2+8, calculate the following values. If the answer is undefined, write DNE. f(8)=f(8)=f(8)= □\square□ f(−6)=f(-6)=f(−6)= □\square□ f(0)=f(0)=f(0)= □\square□

Studdy Solution

STEP 1

STEP 2

1. Calculate f(8)f(8)f(8)2. Calculate f(−6)f(-6)f(−6)3. Calculate f(0)f(0)f(0)

STEP 3

Let's **substitute** x=8x = 8x=8 into our function f(x)=−3x2+8f(x) = -3x^2 + 8f(x)=−3x2+8.This gives us f(8)=−3⋅(8)2+8f(8) = -3 \cdot (8)^2 + 8f(8)=−3⋅(8)2+8.

STEP 4

First, we **square** the 8\textbf{8}8: (8)2=64(8)^2 = 64(8)2=64.So, f(8)=−3⋅64+8f(8) = -3 \cdot 64 + 8f(8)=−3⋅64+8.

STEP 5

Next, we **multiply** −3-3−3 by 646464: −3⋅64=−192-3 \cdot 64 = -192−3⋅64=−192.So, f(8)=−192+8f(8) = -192 + 8f(8)=−192+8.

STEP 6

Finally, we **add** −192-192−192 and 888: −192+8=−184-192 + 8 = -184−192+8=−184.So, f(8)=-184f(8) = \textbf{-184}f(8)=-184.

STEP 7

Now, let's **substitute** x=−6x = -6x=−6 into our function: f(−6)=−3⋅(−6)2+8f(-6) = -3 \cdot (-6)^2 + 8f(−6)=−3⋅(−6)2+8.

STEP 8

We **square** −6-6−6: (−6)2=36(-6)^2 = 36(−6)2=36.Remember, a negative times a negative is a positive!So, f(−6)=−3⋅36+8f(-6) = -3 \cdot 36 + 8f(−6)=−3⋅36+8.

STEP 9

Next, we **multiply** −3-3−3 by 363636: −3⋅36=−108-3 \cdot 36 = -108−3⋅36=−108.So, f(−6)=−108+8f(-6) = -108 + 8f(−6)=−108+8.

STEP 10

Finally, we **add** −108-108−108 and 888: −108+8=−100-108 + 8 = -100−108+8=−100.So, f(−6)=-100f(-6) = \textbf{-100}f(−6)=-100.

STEP 11

Let's **substitute** x=0x = 0x=0 into our function: f(0)=−3⋅(0)2+8f(0) = -3 \cdot (0)^2 + 8f(0)=−3⋅(0)2+8.

STEP 12

Anything multiplied by zero is zero, so −3⋅(0)2=−3⋅0=0-3 \cdot (0)^2 = -3 \cdot 0 = 0−3⋅(0)2=−3⋅0=0.This simplifies our equation to f(0)=0+8f(0) = 0 + 8f(0)=0+8.

STEP 13

Adding zero to any number doesn't change the number, so 0+8=80 + 8 = 80+8=8.Therefore, f(0)=8f(0) = \textbf{8}f(0)=8.

STEP 14

f(8)=−184f(8) = -184f(8)=−184 f(−6)=−100f(-6) = -100f(−6)=−100 f(0)=8f(0) = 8f(0)=8

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionGiven the function $f(x)=-3 x^{2}+8$ , calculate the following values. If the answer is undefined, write DNE. $f(8)=$ $\square$ $f(-6)=$ $\square$ $f(0)=$ $\square$

1. Calculate $f(8)$
2. Calculate $f(-6)$
3. Calculate $f(0)$

Let's substitute $x = 8$ into our function $f(x) = -3x^2 + 8$ .
This gives us $f(8) = -3 \cdot (8)^2 + 8$ .

First, we square the $\textbf{8}$ : $(8)^2 = 64$ .
So, $f(8) = -3 \cdot 64 + 8$ .

Next, we multiply $-3$ by $64$ : $-3 \cdot 64 = -192$ .
So, $f(8) = -192 + 8$ .

Finally, we add $-192$ and $8$ : $-192 + 8 = -184$ .
So, $f(8) = \textbf{-184}$ .

Now, let's substitute $x = -6$ into our function: $f(-6) = -3 \cdot (-6)^2 + 8$ .

We square $-6$ : $(-6)^2 = 36$ .
Remember, a negative times a negative is a positive!
So, $f(-6) = -3 \cdot 36 + 8$ .

Next, we multiply $-3$ by $36$ : $-3 \cdot 36 = -108$ .
So, $f(-6) = -108 + 8$ .

Finally, we add $-108$ and $8$ : $-108 + 8 = -100$ .
So, $f(-6) = \textbf{-100}$ .

Let's substitute $x = 0$ into our function: $f(0) = -3 \cdot (0)^2 + 8$ .

Anything multiplied by zero is zero, so $-3 \cdot (0)^2 = -3 \cdot 0 = 0$ .
This simplifies our equation to $f(0) = 0 + 8$ .

Adding zero to any number doesn't change the number, so $0 + 8 = 8$ .
Therefore, $f(0) = \textbf{8}$ .

$f(8) = -184$ $f(-6) = -100$ $f(0) = 8$