A quadratic function in vertex form looks like `f(x)=a(x-b)^2+c` where (b,c) is the vertex. That means that for this question, b=-2 and c=7. To find a, we substitute the y-intercept (0,-3) into the function.
`-3=a(0+2)^2+7` simplify the brackets
`-3=4a+7` move 7 to other side
`-10=4a` divide by 4 and simplify
This means the quadratic function is `f(x)=-5/2(x+2)^2+7` .
If it is necessary to write the function in standard form, we need to expand the brackets and simplify.
The function is `f(x)=-5/2(x+2)^2+7` or `f(x)=-5/2x^2-10x-3` .