MathsNet: Interactive Graphs: curves

Curves: quadratic
Choose values for a and b and observe the values of

y = ax²+b

a =		b =
x	-4	-3	-2	-1	0	1	2	3	4
x²
ax²+b

Use this table to solve:	2x²+1 = 9	x=
	3x² - 1 = 26	x=
	4x²+6 = 10	x=
	2x² - 5 = 13	x=
	4x²+8 = 72	x=

Here is a plot of some points from a quadratic equation.

What you should understand

When a=1, b=0, the table shows values of y = x². Notice how the values decrease and increase in a symmetric way. When plotted this equation produces a symmetriuc graph where the y-axis is the line of symmetry.
Equations like those above that you had to solve are called quadratic equations. There are usually 2 possible answers for each one.