# 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

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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` .**