Question

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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 ✓

Answer 1

Answer:q = - 9 and r = - 10

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!!! ❤️