Question

How do you find the vertex of a quadratic equation?

Answer 1

Find the vertex of a quadratic equation?

A quadratic equation is written as $a{x}^2+bx+c$ in its standard form. And the vertex can be found by using the formula $-\frac{b}{2a}$.
For example, let's suppose our problem is to find out the vertex $(x,y)$ of the quadratic equation $x^2+2x-3$.

Assess the value of $\mathrm{a},\mathrm{b}\mathrm{and}\mathrm{c}$. In this example, $a=1,b=2\mathrm{and}c=-3$.

Plug your values into the formula $-\frac{b}{2a}$.

For this example, $-\frac{b}{2a}=-\frac{2}{2·1}=-1$.

The $x$-coordinate of your vertex is $-1$. Now plug in $-1$ for $x$ in the equation $x^2+2x-3$ to find out the $y$-coordinate.

The $y$-coordinate is:

$\begin{array}{rcl}{x}^2+2x-3& =& {(-1)}^2+2\left(-1\right)-3\\ & =& 1-2-3\\ & =& -4\end{array}$

So, the vertex of equation $x^2+2x-3$is $\left(-1,-4\right)$.

Therefore, the vertex can be found by using the formula $\mathbf{-}\frac{\mathbf{b}}{\mathbf{2}\mathbf{a}}$.