Question

How do I determine quadratic function f, whose graph is vertex (1,-2) and passes thru (3,6)

Answer 1

Let the quadratic function be of the genera form

\[ f(x)=ax^2+bx+c\]
Then match the three unknown coefficients to the points

\[f(1)=-2 \\ f(3)=6\]
And for the Vertex

\[1 = \frac{-b}{2a} \rightarrow 2a=-b \]
Then solve system of equation

Answer 2

ok, but how do I plug my numbers in

Answer 3

\[f(1)=a+b+c=-2 \\
f(3)=9a+3b+c = 6 \\2a=-b \]

Answer 4

System of equations, three unknowns, three equations, therefore one definite solution, because none of the equations above is redundant.

Answer 5

i still don't understand

Answer 6

Do you know how to solve a system of linear equations?