Gerald is testing a computer graphics program. He needs to insert a parabolic shape by transforming the quadratic parent function, f(x) = x2. Gerald needs the parabolic shape to open downward, stretch vertically by a factor of 2, shift right by 3 units, and shift down by 4 units. Which transformed function should Gerald enter into the computer graphics program to achieve this result?
g(x) = –2(x – 3)2 – 4
g(x) = 2(x – 3)2 – 4
g(x) = –2(x + 3)2 – 4
g(x) = 2(x + 3)2 – 4

Function, Gerald should enter to the computer is g(x) = -2(x + 3)² - 4

Correct option is C.

Transformations are changes done in the shapes on a coordinate plane by rotation or reflection or translation.

Given,

Parent function f(x) = x²

g(x) = ?

for reflection over x - axis,

g(x) = -f(x)

g(x) = -x²

For vertical stretch of factor a.

g(x) = a f(x)

g(x) = -2x²

For right shift by a

g(x) = f(x + a)

g(x) = -2(x + 3)²

Shift down by b units

g(x) = f(x) - b

g(x) = -2(x + 3)² - 4

Hence, g(x) = -2(x + 3)² - 4 is the function, Gerald should enter.

Learn more about transformation here:

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