Question

Now you try. If you have a parabola

with a vertex of (1,-4) and passes
through point (-2,-1), what is "a"?
-1/3
10
2
1/3

Answer 1

Answer: 1/3

Work Shown

(h, k) = (1,-4) = vertex

(x, y) = (-2,-1) = another point on the parabola

y = a(x-h)^2 + k ........ vertex form

-1 = a(-2-1)^2 - 4

-1 = a(-3)^2 - 4

-1 = 9a - 4

9a-4 = -1

9a = -1+4

9a = 3

a = 3/9

a = 1/3

The vertex form would be y = (1/3)(x-1)^2 - 4

which is the same as writing
`y = (1)/(3)(\text{x}-1)^2-4`

Because a > 0, the parabola opens upward to make the vertex (1,-4) the lowest point on the parabola.