Graphing y=ax²+bx

The bx bx is included and the c term is omitted. The most dramatic effect of the bx term is that the axis of symmetry is moved away from the center of the graph. Read on and complete the exercise to fully understand how to calcuate the solutions, the axis of symmetry, and vertex. But before diving into the nitty gritty of graphing such quadratic equations, we need to cover factorisation.

Factorisation is the reverse of expanding brackets. The brackets are expanded below; now imagine you are now upside down and read the two lines of algebra in reverse, this is known as factorisation. Press the reverse button to alternate between expansion of brackets and factorisation.

The timestable should be etched into your mind to get a thorough appreciation of numbers, and this will help you to factorise equation, so don't use your calculator for the exercise below.

Imagine you have been given some graph paper and a quadratic equation to sketch. You could trace the curve by creating a table of coordinates by picking many x values and calculating the y-value; this would be far too time consuming and the slider lets you trace points on the curve. There are 4 steps, press the buttons in sequence to view these steps.

Use the sliders to input the solutions, axis of symmetry, and vertex for the quadratic equation. The final step of sketching the quadratic equation should be done on paper.

check you working out below:

Summary

The quadratic equation of the form y=ax²+bx (where c=0), has one solution x=0 and another solution equal to a non zero number. The axis of symmetry is a vertical line that crosses the midpoint of the solutions. The vertex is on the axis of symmetry the minimum or maximum point of the quadratic curve.