Question

PLEASE HELP!!! PLZ!!!

Which of the following equations describes the graph!!?!?

A.

`y = (1)/(3) x ^(2) + 1`
B.

`y = - (1)/(3) x ^(2) + 1`
C.

`y = - (1)/(3) x ^(2) - 1`
D.

`y = (1)/(3) x ^(2) - 1`

Answer 1

We can use the vertex form

`y = a {(x - h)}^(2) + k`
to find the equation of the graph. We know that a is the coefficient, and since the graph opens upwards and is slightly stretched vertically, we know that a is 1/3. On the graph, we see that the vertex of the parabola is at (0,-1). Therefore, h is 0 and k is -1.
Our vertex form equation is

`y = (1)/(3) {x}^(2) - 1`
Which is D