Question

Function g is a transformation of the parent function f(x) = x2. The graph of fis reflected across the x-axis, and then translated left 4 units anddown 2 units to form the graph of gWrite the equation for g in the form y = ax2 + bx + cO A. y = -x2 + 8x + 14O B. y = -x2 - 8x - 18O C. y = x2 - 8x + 18O D. y = -x2 - 8x + 14

Answer 1

The parent function is given as:

f(x) = x²

y = x²

The graph is reflected across the x - axis

The x axis remains the same but the y axis is negated

g(x) = -x²

It is translated 4 units left

The function g(x) becomes

g(x) = -(x - 4)²

It is the translated 2 units down

g(x) = -(x - 4)² - 2

Simplifying the above equation:

g(x) = - (x² - 8x + 16) - 2

g(x) = -x² + 8x - 16 - 2

g(x) = -x² + 8x - 18