Question

Find the quadratic function that has vertex (-1, 8) and whose graph goes through the point (8, 170).

I could not understand this problem I Can not for the lift of me get it. I got as far as some number(x+1)^2+8 but i don't know what the number before all that would be for the vertical stretch

Answer 1

remember the form, y = a(x-h)^2 + k
where (h,k) is the vertex, and x and y are points on the graph,,
therefore, solving for a,
170 = a*(8-(-1))^2 + 8
170 = a*81 + 8
81a = 162
a = 2
therefore,
y = 2(x+1)^2 + 8
expanding this,
y = 2x^2 + 4x + 10

so there,, :)

Answer 2

Thank you so much!!!