Question

A parabola opening up or down has vertex (0, -4) and passes through (10, 1). Write its

equation in vertex form.

Answer 1

Since the vertex is (0, -4), we know that the equation of the parabola will have the form:

y = a(x - 0)^2 - 4

where "a" is the coefficient that determines whether the parabola opens up or down.

To find the value of "a", we can use the fact that the parabola passes through the point (10, 1):

1 = a(10 - 0)^2 - 4

1 + 4 = 100a

5 = 100a

a = 1/20

Substituting this value of "a" into the equation for the vertex form, we get:

y = (1/20)x^2 - 4

So the equation of the parabola in vertex form is y = (1/20)x^2 - 4, with vertex (0, -4) and passing through (10, 1).

Explanation: