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Curves: solving
A quadratic curve is shown. Move the red point to change it. The places where it crosses the x axis are marked.
Please enable Java for an interactive construction (with Cinderella).
Move the red point so that the curve crosses the x axis at:
x = -1 and x = 7
coordinates of the red point:
x = -3 and x = 5
coordinates of the red point:
x = 6 only
coordinates of the red point:
x = -6 and x = 4
coordinates of the red point:
What you should understand

Equations of the form ax²+bx+c = 0 are called quadratic equations.

To solve them you can plot
y = ax²+bx+c
on a graph and find where this quadratic curve crosses the x axis.

The above display shows that a quadratic curve can cross the x axis in 1 or 2 places, and may not cross the x axis at all. This tells you that the equation ax²+bx+c = 0 can have either 0, 1 or 2 answers.

a1 a2 a3 a4
b1 b2 b3 b4
c1 c2 c3 c4
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