Verex form of a quadratic function

Consider the following function f(x)=-4x^2+4x+3. Change f(x) into vertex form. 

Algebra
Laiba Khan Laiba Khan
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1 Answer

We try to write this fuunction $f(x)=-4x^2+4x+3$ in the vertex form $y = a(x - h)^2+ k$. 

We will do this by factoring the coefficient of $x^2$ first and then completing the square: 
\[f(x)=-4x^2+4x+3=-4(x^2-x-\frac{3}{4})\]
\[=-4(x^2-x+\frac{1}{4}-\frac{3}{4}-\frac{1}{4})\]
\[=-4(x^2-x+\frac{1}{4}-1)\]
\[=-4((x-\frac{1}{2})^2-1)\]
\[=-4(x-\frac{1}{2})^2+4,\]
which is in the vertex form.

Halie10 Halie10
  • Halie10 Halie10
    0

    There was a mistake in my solution. I have revised it.

    • M F H M F H
      +1

      also, it's vertex , not vortex. ;-)

    • Halie10 Halie10
      0

      Thank you, M F H. I fixed the typo.

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