Question

A quadratic function has its vertex at the point (2,3). The function passes through the point (3,9). Find the quadratic and linear coefficients and the constant term of the function

Answer 1

I found the quadratic coefficient is 6 but my other answers were wrong

Answer 2

The function is y = x^2 -5x +6

Answer 3

th quadratic coefficient is 1 and the linear coefficient is -5

Answer 4

A quadratic can be written as \(f(x) =a(x-h)^{2} + k\) where (h,k) is the vertex. So it tells you your vertex is (2,3) and that the point (3,9) exists. So h must be 2 and k must be 3, giving you \(f(x) = a(x-2)^{2} + 3\) Now the second point says that when x is 3, f(x) = 9. So now just plug in 3 for x and 9 for f(x) and solve for a:
\(9=a(3-2)^{2} + 3\)