Question

Consider a parabola P that is congruent to y=x^2, opens upward, and has vertex (0,0). Find the equation of a new parabola that results if P is reflected in the x-axis, and translated 1 unit to the left and 3 units up.

Answer 1

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Answer:

y = -(x+1)^2 +3

Explanation:

Translating f(x) left by 1 unit replaces x with x+1.

Translating f(x) up by 3 units replaces f(x) with f(x)+3.

Reflecting f(x) over the x-axis replaces f(x) with -f(x).

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When y = x^2 is reflected over the x-axis, it becomes ...

y = -x^2

When y = -x^2 is translated 1 unit left, it becomes ...

y = -(x +1)^2

When y = -(x+1)^2 is translated 3 units up, it becomes ...

y = -(x +1)^2 +3