Math / Algebra

Question7. \#ACTPREP For the function $g$ defined below, $a$ is a constant and $g(4)=8$ . What is the value of $g(-4)$ ? $g(x)=a x^{2}+24$ A) 56 B) 40 C) 8 D) -1 E) -8
9. Given $\triangle A B C$ with

Studdy Solution

STEP 1

1. The function $g(x) = ax^2 + 24$ is given.
2. $a$ is a constant.
3. $g(4) = 8$ .
4. We need to find the value of $g(-4)$ .

STEP 2

1. Use the given function to create an equation with the known value $g(4) = 8$ .
2. Solve for the constant $a$ .
3. Substitute $a$ back into the function to find $g(-4)$ .

STEP 3

Use the given function to create an equation with the known value $g(4) = 8$ .
Substitute $x = 4$ into the function:
$g(4) = a(4)^2 + 24 = 8$

STEP 4

Solve for the constant $a$ .
$16a + 24 = 8$
Subtract 24 from both sides:
$16a = 8 - 24$ $16a = -16$
Divide both sides by 16:
$a = \frac{-16}{16}$ $a = -1$

STEP 5

Substitute $a$ back into the function to find $g(-4)$ .
Substitute $a = -1$ and $x = -4$ into the function:
$g(-4) = (-1)(-4)^2 + 24$
Calculate:
$g(-4) = (-1)(16) + 24$ $g(-4) = -16 + 24$ $g(-4) = 8$
The value of $g(-4)$ is:
$\boxed{8}$

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Question7. \#ACTPREP For the function $g$ defined below, $a$ is a constant and $g(4)=8$ . What is the value of $g(-4)$ ? $g(x)=a x^{2}+24$ A) 56 B) 40 C) 8 D) -1 E) -8
9. Given $\triangle A B C$ with

Studdy Solution

STEP 1

1. The function $g(x) = ax^2 + 24$ is given.
2. $a$ is a constant.
3. $g(4) = 8$ .
4. We need to find the value of $g(-4)$ .

STEP 2

1. Use the given function to create an equation with the known value $g(4) = 8$ .
2. Solve for the constant $a$ .
3. Substitute $a$ back into the function to find $g(-4)$ .

STEP 3

Use the given function to create an equation with the known value $g(4) = 8$ .
Substitute $x = 4$ into the function:
$g(4) = a(4)^2 + 24 = 8$

STEP 4

Solve for the constant $a$ .
$16a + 24 = 8$
Subtract 24 from both sides:
$16a = 8 - 24$ $16a = -16$
Divide both sides by 16:
$a = \frac{-16}{16}$ $a = -1$

STEP 5

Substitute $a$ back into the function to find $g(-4)$ .
Substitute $a = -1$ and $x = -4$ into the function:
$g(-4) = (-1)(-4)^2 + 24$
Calculate:
$g(-4) = (-1)(16) + 24$ $g(-4) = -16 + 24$ $g(-4) = 8$
The value of $g(-4)$ is:
$\boxed{8}$

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Question7. \#ACTPREP For the function ggg defined below, aaa is a constant and g(4)=8g(4)=8g(4)=8. What is the value of g(−4)g(-4)g(−4) ? g(x)=ax2+24g(x)=a x^{2}+24g(x)=ax2+24 A) 56 B) 40 C) 8 D) -1 E) -89. Given △ABC\triangle A B C△ABC with

Studdy Solution

STEP 1

1. The function g(x)=ax2+24 g(x) = ax^2 + 24 g(x)=ax2+24 is given.2. a a a is a constant.3. g(4)=8 g(4) = 8 g(4)=8.4. We need to find the value of g(−4) g(-4) g(−4).

STEP 2

1. Use the given function to create an equation with the known value g(4)=8 g(4) = 8 g(4)=8.2. Solve for the constant a a a.3. Substitute a a a back into the function to find g(−4) g(-4) g(−4).

STEP 3

Use the given function to create an equation with the known value g(4)=8 g(4) = 8 g(4)=8.Substitute x=4 x = 4 x=4 into the function:g(4)=a(4)2+24=8 g(4) = a(4)^2 + 24 = 8 g(4)=a(4)2+24=8

STEP 4

Solve for the constant a a a.16a+24=8 16a + 24 = 8 16a+24=8Subtract 24 from both sides:16a=8−24 16a = 8 - 24 16a=8−24 16a=−16 16a = -16 16a=−16Divide both sides by 16:a=−1616 a = \frac{-16}{16} a=16−16​ a=−1 a = -1 a=−1

STEP 5

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Question7. \#ACTPREP For the function $g$ defined below, $a$ is a constant and $g(4)=8$ . What is the value of $g(-4)$ ? $g(x)=a x^{2}+24$ A) 56 B) 40 C) 8 D) -1 E) -8
9. Given $\triangle A B C$ with

1. The function $g(x) = ax^2 + 24$ is given.
2. $a$ is a constant.
3. $g(4) = 8$ .
4. We need to find the value of $g(-4)$ .

1. Use the given function to create an equation with the known value $g(4) = 8$ .
2. Solve for the constant $a$ .
3. Substitute $a$ back into the function to find $g(-4)$ .

Use the given function to create an equation with the known value $g(4) = 8$ .
Substitute $x = 4$ into the function:
$g(4) = a(4)^2 + 24 = 8$

Solve for the constant $a$ .
$16a + 24 = 8$
Subtract 24 from both sides:
$16a = 8 - 24$ $16a = -16$
Divide both sides by 16:
$a = \frac{-16}{16}$ $a = -1$