What is the vertex form of #y=6x^2+13x+3 #?
The general formula for vertex form is
You can also find the answer by completing the square, the general formula is found by completing the square in using
The vertex form is given by
This form highlights the transformations that the function
The vertex form is also form in which a quadratic function can be directly solved algebraically (if it has a solution). So getting a quadratic function into vertex form from standard form, called completing the square, is the first step to solving the equation.
The key to completing the square is building a perfect square in ANY quadratic expression. A perfect square is of the form
COMPLETING THE SQUARE
You start with
factor out the 6
Multiply and divide the linear term by 2
This lets us see what our
To build our perfect square we need the
we add this to our expression, but to avoid changing the value of anything we must subtract it too, this creates an extra term,
We gather up our perfect square
and replace it with
We multiple out our extra to to get it outside the brackets.
Play with some fractions to neaten
And we have
If we want to in the identical form as above
The general formula used above is from doing the above with