Question

A parabola opening up or down has vertex (0,-7) and passes through (4,-3). Write its equation in vertex form

Answer 1

Answer:

y = $\frac{1}{4}$ x² - 7

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Here (h, k) = (0, - 7), thus

y = a(x - 0)² - 7

To find a substitute (4, - 3) into the equation

- 3 = a(4 - 0)² - 7, that is

- 3 = 16a - 7 ( add 7 to both sides )

4 = 16a ( divide both sides by 16 )

a = $\frac{1}{4}$, thus

y = $\frac{1}{4}$ x² - 7