Question

whats the vertex of the function y=x^2-14+13

Answer 1

We have a formula for getting the vertex of a quadratic equation of the form
\[\Large y = \color{red}ax^2 + \color{blue}bx + \color{green}c\]
And that is this point:
\[\huge \left(-\frac{\color{blue}b}{2\color{red}a}\quad , \quad \frac{4\color{red}a\color{green}c - \color{blue}b^2}{4\color{red}a}\right)\]

Answer 2

And all you have to do now is plug in the appropriate values for \(\color{red}a , \color{blue}b,\) and \(\color{green}c\)

Answer 3

Alternatively, you can complete the square. You'll go from
\[y=ax^2+bx+c\]
to
\[y=a(x-h)^2+k,\]
where \((h,k)\) is the vertex and
\[(h,k)=\left(-\frac{\color{blue}b}{2\color{red}a}\quad , \quad \frac{4\color{red}a\color{green}c - \color{blue}b^2}{4\color{red}a}\right)\]