quadratici functions

[j poindexter]

i need help with this question pls
.find the quadratic function y=f(x) that has the given vertex and whose graph passes through the given point. write the function in standard form.
vertex (0,0); passes through (1,3)

 

[alohacharlie]

The equation for a quadratic function with vertex at ( h, k ) is f(x) = a (x - h)^2 + k

f(x) = a( x - h )^2 + k

y = a ( x - 0 )^2 + 0 substitute in the h and k values given

y = a (x)^2

3 = a (1)^2 Substitute in the x and y values given

So now you know the value of a

Substitute it into the equation f(x) = a( x - h )^2 + k along with the given vertex and you will have the equation