Graphs of Quadratic Equations

A quadratic equation is one with an x2 term. It may also have an x  term and a numerical term.

The general formula for a quadratic is:  ax2 + bx + c  (a, b and c are constants)

When you graph a quadratic equation, the shape of the graph is called a parabola. This is a u-shaped curve.

Above is the graph of y = x2

It passes through the origin. The point with the lowest y-value is called the minimum. This is said to be the turning point of the graph, and the gradient is zero here.

The graph of y = x2 – 2 will pass through the point (0, -2). It cuts through the x-axis at two points. By finding the x-co-ordinates of where the graph cuts through the x-axis, you can solve the quadratic equation. (On the x-axis, y = 0)

Using this technique, we can deduce that there is only one solution to y = x2 , which is x = 0

 The graph of y = -x2 is still a parabola, but it is inverted. Instead of having a minimum point, it has a
maximum, the point where the y-value is the highest. Quadratic equations with negative coefficients
of  x2 can still be solved by looking at the x-axis intercept.

A parabola which does not touch or intercept the x-axis represents a quadratic equation which has no solutions.

Other methods to solve quadratic equations:

Factorisation

Using the Quadratic Formula


To get to grips with quadratic equations even more, visit this quadratic equation grapher