Question

Two open, downward facing parabolas of different sizes that share a vertex are plotted on a coordinate plane. 1 is a solid line and 1 is a dotted line.
Identify the value of k
for the vertical stretch from the original function (solid parabola) to the dilated function (dotted parabola).

(1 point)
k=

Answer 1

I don't have the graph, so I can't read off the numeric value. I can tell you how to find k from the picture:

- Pick any x-value where you can read the y-values of both curves (not the shared vertex).
- Let y_s be the y-value of the solid (original) parabola at that x, and y_d be the y-value of the dotted (dilated) parabola at the same x.
- Because the dilation is vertical about the shared vertex, k = y_d / y_s.

(If the vertex is at the origin and the original is y = a x^2, the dilated is y = (k a) x^2 and k is the ratio of the parabola coefficients; numerically this is the same as the ratio of y-values.)

If you paste the image or give one pair of corresponding points (x, y_s) and (x, y_d), I will compute k.