if the parabola represented by the equation y=(x-5)^2-7 is shifted left two units and down one unit, what is the equation of the new location of the parabola?

Question

y=(x-3)^2-8

y=(x-3)^2-6

y=(x-7)^2-8

y=(x-7)^2-6

Answer 1

The correct answer is y=(x-3)²-8

An equation of a parabola can be represented by the general equation: y=n(x-h)²+k, where (h,k) represents the parabola's vertex and n represents the parabola's dilation factor (tells you where the parabola will be facing up or down and whether it will be wider or thinner).

The equation currently is y=(x-5)²-7, therefore my h=5 and my k=-7, or in other words my vertex is (5,-7). The parabola is shifted to the left 2 units to the left, thus the new x-coordinate of the vertex will be 3 and the parabola is shifted on unit down, thus the new y-coordinate of the vertex will be -8.

Since the vertex of the new parabola is (3,-8), that means my h=3 and my k=-8. Plugging that into the equation y=n(x-h)²-k, we get y=(x-3)²-8.