Question

A parabola opening up or down has vertex

(-4, -6) and passes through (-14, 13/2)
Write its equation in vertex form.

Answer 1

To write the equation of the parabola in vertex form, we use the standard form:

y = a(x - h)^2 + k, where (h, k) is the vertex.

Given that the vertex is (-4, -6), we have:

h = -4 and k = -6

Now, we need to find the value of "a" using the point (-14, 13/2) which lies on the parabola.

Substituting the values in the standard form, we get:

13/2 = a(-14 - (-4))^2 - 6

Simplifying, we get:

13/2 = 100a - 6

100a = 13/2 + 6

a = 19/200

Therefore, the equation of the parabola in vertex form is:

y = (19/200)(x + 4)^2 - 6

Explanation: