Quadratic function

Question

The quadrate function f (x ) has vertex (1.8, 21); f(x) = A * x ^ 2 + 14.4x + c what are numerical values of A and C

Answer 1

A quadratic function is in the form of

f(x) = (x-h)²+k where (h,k) is the vertex, in this case (1.8, 21). This requires completing the square to convert ax²+bx+c into (x-h)²+k.

h = -b/2a = 7.2/a=-h=-1.8 --> a = -4

k = c-b²/(4a) = c+14.4²/16 = 21 --> c = 8.04

Answer 2

f(x) = a(x - 1.8)² + 21 Vertex Form

21 = a(1.8)² +14.4(1.8) + c Given point form

Two equatios in two unknows. Can you solve the system and answer?