If you apply the changes below to the quadratic parent function, f(x)=x^2 which of these is the equation of the new function?

*shift 3 units left

*vertically stretch by a factor of 4

*reflect over the x-axis

( need answer asap! )

A

Step-by-step explanation:

Given the parent function y = x², then

y = (x + a) represents a horizontal translation

• If a > 0 , then shift to the left of a units

• If a < 0, then shift to the right of a units

Thus a shift of 3 units left ⇒ y = (x + 3)²

A vertical stretch of a units, stretches away from the x- axis

A vertical compression of a units, compresses towards the x- axis

• | a | > 1 is a stretch

• 0 < | a | < 1 is a compression

Thus a vertical stretch of 4 ⇒ y = 4(x + 3)²

A reflection in the x- axis, negates the y- coordinate

y = - 4(x + 3)² → A

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