Question

Image: A curved line with coordinate points at -1, 3 and another at 3, -1 and the final one at -5, -1.

write an equation for the function in vertex form.

Answer 1

Vertex is at (-1, 3) (midpoint of x = -5 and x = 3). Use vertex form y = a(x - h)^2 + k with (h,k)=(-1,3):

y = a(x + 1)^2 + 3.

Use (3, -1) to find a: -1 = a(3+1)^2 + 3 = 16a + 3 → 16a = -4 → a = -1/4.

So the equation is y = -(1/4)(x + 1)^2 + 3.