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2
The parent function of a quadratic, f(x) = x is reflected across the
2
x-axis, vertically compressed by a factor of 3, translated 8 units left
and 16 units up. Write the equation of the transformed quadratic
function, g(x), in vertex form.
g(x) =
² x 160 qx x ✓

q = - 9 and r = - 10

Step-by-step explanation:

since g(x) is divided by (x - 1) with remainder - 12, then (1) = 4(1)³ + q(1)² + r + 3 = - 12, that is 4 + q + r + 3 = - 12

q + r + 7 = - 12 ( subtract 7 from both sides )

q + r = - 19 → (1)

Since (x - 3) is a factor of g(x), then

g(3) = 4(3)³ + q(3)² + 3r + 3 = 0, that is

108 + 9q + 3r + 3 = 0

9q + 3r + 111 = 0 ( subtract 111 from both sides )

9q + 3r = - 111 → (2)

The 2 equations to be solved simultaneously are (1) and (2)

Multiply (1) by - 3

- 3q - 3r = 57 → (3)

Add (2) and (3) term by term to eliminate r

6q = - 54 ( divide both sides by 6 )

q = - 9

Substitute q = - 9 into (1)

- 9 + r = - 19 ( add 9 to both sides )

r = - 10

Hope the helps!!! ❤️

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step-by-step explanation:

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answer: solve 5\cdot 2^x=2405⋅2  

x

=2405, dot, 2, start superscript, x, end superscript, equals, 240.

solution

to solve for xxx, we must first isolate the exponential part. to do this, divide both sides by 555 as shown below. we do not multiply the 555 and the 222 as this goes against the order of operations!

\begin{aligned} 5\cdot 2^x& =240 2^x& =48 \\ \end{aligned}  

5⋅2  

x

2  

x

​    

=240

=48

​

step-by-step explanation: