A parabola is shown graphed to the right that is a transformation of y= x^2. the transformation includes a vertical stretch and a verticle shift. what are the stretch and shift

Question

Based on your answer, write an equation for this parabola

the points given are

(-2, 1)

(-1,-5)

(0,-7)

(1,-5)

(2,1)

Answer 1

We can actually solve this problem very simply.

Looking at the matched values of y for x=˜±1 and ±2, we see that the axis of symmetry is x =0

Thus, our vertex is (0.-7), and the value of y is 2 greater when x increases/decreases by 1;thus, our parabola is

y = 2x^2 -7.

At x = ±2, this would yield a value of y of 1, which matches this value as well, a check.