If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

The graph of a quadratic function is a parabola, which is a "u"-shaped curve. In this article, we review how to graph quadratic functions.
The graph of a quadratic function is a parabola, which is a "u"-shaped curve:
Looking for an introduction to parabolas? Check out this video.

### Example 1: Vertex form

Graph the equation.
$y=-2\left(x+5{\right)}^{2}+4$

This equation is in vertex form.
$y=a\left(x-h{\right)}^{2}+k$
This form reveals the vertex, $\left(h,k\right)$, which in our case is $\left(-5,4\right)$.
It also reveals whether the parabola opens up or down. Since $a=-2$, the parabola opens downward.
This is enough to start sketching the graph.
To finish our graph, we need to find another point on the curve.
Let's plug $x=-4$ into the equation.
$\begin{array}{rl}y& =-2\left(-4+5{\right)}^{2}+4\\ \\ & =-2\left(1{\right)}^{2}+4\\ \\ & =-2+4\\ \\ & =2\end{array}$
Therefore, another point on the parabola is $\left(-4,2\right)$.
Want another example? Check out this video.

### Example: Non-vertex form

Graph the function.
$g\left(x\right)={x}^{2}-x-6$

First, let's find the zeros of the function—that is, let's figure out where this graph $y=g\left(x\right)$ intersects the $x$-axis.
$\begin{array}{rl}g\left(x\right)& ={x}^{2}-x-6\\ \\ 0& ={x}^{2}-x-6\\ \\ 0& =\left(x-3\right)\left(x+2\right)\end{array}$
So our solutions are $x=3$ and $x=-2$, which means the points $\left(-2,0\right)$ and $\left(3,0\right)$ are where the parabola intersects the $x$-axis.
To draw the rest of the parabola, it would help to find the vertex.
Parabolas are symmetric, so we can find the $x$-coordinate of the vertex by averaging the $x$-intercepts.
With the $x$-coordinate figured out, we can solve for $y$ by substituting into our original equation.
$\begin{array}{rl}g\left(0.5\right)& =\left(0.5{\right)}^{2}-\left(0.5\right)-6\\ \\ & =0.25-0.5-6\\ \\ & =-6.25\end{array}$
Our vertex is at $\left(0.5,-6.25\right)$, and our final graph looks like this:
Want another example? Check out this video.

## Practice

Problem 1
Graph the equation.
$y=2\left(x+1\right)\left(x-1\right)$

Want more practice graphing quadratics? Check out these exercises: