find a quadratic function whose graph has a max of 25 and x-intercepts of -3 and 2.

Answer 1

(-3,0), (2,0).

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

h = (-3+2) / 2 = -1/2.

y = a(2-(-1/2))^2 + 25,
25a/4 + 25 = 0,
25a + 100 = 0,
25a = -100,
a = -4.

y = -4(x+1/2)^2 + 25 = Vertex form.

y = -4(x^2 + x + 1/4) + 25,
y = -4x^2 - 4x - 1 +25,
y = -4x^2 - 4x + 24,