Quadratic Graphs

A quadratic graph represents a quadratic function of the form $f(x)=a{x}^2+bx+c$ and you will need to be familiar with every aspect of the graph.

Shape of the Graph

If $a>0$, the parabola opens upwards, resembling a "U" shape (a positive quadratic).

If $a<0$, the parabola opens downwards, resembling an upside-down "U" or an 'n' (a negative quadratic).

X-Intercepts (Roots)

The x-intercepts of the graph, also known as the roots, are the points where the graph intersects the x-axis. These can be found by solving the quadratic equation.

Y-Intercept

The y-intercept is the point where the graph intersects the y-axis.

It can be found by evaluating the function at $x=0$:

The turning point

This is the highest or lowest point, depending on the direction the parabola opens.

It can be found with:

$$x=-\frac{b}{2a}$$

To find the corresponding $y$-coordinate, substitute this value of $x$ back into the function.