# determine the quadratic function f whose graph is given the vertex(-2,7) and the y intercept is -3 simplify f(x) = must show work 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...

Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

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

`a=-5/2`

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.

`f(x)=-5/2(x^2+4x+4)+7`

`=-5/2x^2-10x-10+7`

`=-5/2x^2-10x-3`

The function is `f(x)=-5/2(x+2)^2+7` or `f(x)=-5/2x^2-10x-3` .

Approved by eNotes Editorial Team