Quadratic Graphs

A quadratic graph represents a quadratic function of the form \(f(x) = ax^2 + bx + c\) 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.