Question

What is the equation of the graph below?

Answer 1

This is a parabola. So start with the vertex formula:

\( y = a(x – h)^2 + k \)

where the vertex is (h,k)

Is that enough?

Answer 2

Is it y = 1(x - 3)^2 - 2?

Answer 3

Or maybe y = -1(x + 2)^2 - 3?

Answer 4

by inspection from the graph, the vertex is at (-2,-3) so h=-2 k=-3

Answer 5

So the second?

Answer 6

Expand the equation and put it into the desired form:

\( y = a(x – (-2))2 + (-3) \)

Answer 7

This will be in terms of a which is still unknown. (well you know a is negative because the parabola opens downward) Run a couple of test values to determine the value of a. As it is you have a convenient y=intercept to make finding a easy.