Question

write a quadratic function in the vertex form f(x)=a(x-h)^2+k such that the graph of the functions opens up and has a vertex ray (-2,3) and contains the point (-5,12)

Answer 1

f(x) = (x + 2)² + 3

Explanation:

function f(x) = a(x-h)² + k has the vertex point (h, k),

Therefore for vertex (-2, 3) → f(x) = a(x - (-2))² + 3

= a(x + 2)² + 3

now replace x & f(x) with -5 & 12 (the function pass through (-5, 12))

12 = a(-5 + 2)² + 3

9 = a(-3)²

a = 9 ÷ 9

= 1

So, the function f(x) = (x + 2)² + 3