describe the translation y=-2(x-4)^2

Question

what is the translation of that equation?

Answer 1

The "translation" refers to how the graph of the equation is changed from the graph of the basic equation, y=x².

The number added or subtracted inside the parentheses tells us that graph moves left or right. In this case the -4 tells us that it shifts to the right 4 units. (A number added or subtracted outside the parentheses indicates movement up or down; negative would be down.)

The number in front of the parentheses (which gets multiplied by x²) tells us two things: the sign of the number tells us whether the parabola opens up or down, and the number tells us about the vertical stretch. In this case, the negative sign means the parabola opens down, and it is stretched vertically by a factor of 2.

The words in bold describe the translation. I like to graph the equation with my students so they can actually see these changes too.

Hope this helps!

Kathye

Answer 2

The translation of this equation is the following:

y=-2(x²-8x+16)   =>   y = -2x² +16x - 32

This is a quadratic function who's roots are the solutions for the quadratic equation -2x² + 16x - 32 = 0