Question

write the equation for the quadratic function that has the vertex at (1,3) and passes through the point (0,5)

Answer 1

For this quadratic, its vertex form $f(x) = a(x-h)^2+k$ is $f(x) = a(x-1)^2+3$.

To find the value of a, plug in (0,5) and solve. 

$5 = a(0-1)^2+3 \\ a = 2$

The final equation in vertex form is $f(x) = 2(x-1)^2+3$.

In standard form $f(x) = ax^2+bx+c$, the function is $f(x) = 2x^2-4x+5$.