How do i convert to vertex form?  f(x) = -3x^2 +42 -141** ^2 is the exponent

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embizze | High School Teacher | (Level 2) Educator Emeritus

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Convert `f(x)=-3x^2+42x-141` to vertex form:

Vertex form is `f(x)=a(x-h)^2+k` where the vertex is (h,k). We can convert from standard form to vertex form by completing the square:

(1) Factor out -3 so that the leading coefficient is 1:


(2) Take "b" over 2 and square it.


(3) Add and subtract 49 in the function:


(4) `f(x)=-3(x^2-14x+49-2)`


** `x^2-14x+49` is in perfect square trinomial form: `(a-b)^2=a^2-2ab+b^2` where a=x and b=7**

(5) Distribute the -3:

`f(x)=-3(x-7)^2+6` which is vertex form.


The graph of `y=-3x^2+42x-141` showing the vertex at (7,6):