Quadratics curves all have the same basic shape (a parabola) and are always symmetrical.When there is a positive x squared term, the parabola is ‘happy’, when the x squared term is negative, the parabola is ‘sad’ (upside down).
Once you know what shape the curve is, you can think about its crossing points (ie where it crosses the x and y axes). The points where the curve crosses the x-axis are the solutions to the equation when y = 0. We call these the ROOTS. We can normally get the roots by factorising. Sometimes we only get one solution, in which case the curve ‘bounces’ off the x-axis at that point, instead of crossing it.
We can also find out where the equation crosses the y-axis by substituting x = 0 into the equation.
Now we can sketch the curve. Remember, it is always symmetrical. The lowest point of the curve (or the highest point if it is a ‘sad’ parabola) is mid-way between the roots.
After half-term we will look at another method for finding the lowest or highest point of the curve (we do this by completing the square). We will also look at curves that don’t cross the x-axis at all.
We can also find out where the equation crosses the y-axis by substituting x = 0 into the equation.
Now we can sketch the curve. Remember, it is always symmetrical. The lowest point of the curve (or the highest point if it is a ‘sad’ parabola) is mid-way between the roots.
After half-term we will look at another method for finding the lowest or highest point of the curve (we do this by completing the square). We will also look at curves that don’t cross the x-axis at all.