Algebra 2: Quadratic Function

Question

Find the quadratic function that passes through the point (1,165) with a vertex of (-8, 3).

If this problem is doable on a Ti-84, please help figure out how to do this problem on that calculator.

Answer 1

y=a(x+8)^2+3 in vertex form with vertex =(-8,3)=(h,k)

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

through the point (1,165)=(x,y)

165=a(1+8)^2+3 = 81a +3

81a =162

a =162/81=2

f(x)=2(x+8)^2+3

=2(x^2+16x+64)+3

=2x^2+32x+128+3

=2x^2+32x+131