Quadratic graph explorer: y = ax² + bx + c

Slide a, b and c to see how each changes the parabola: a opens or flips it, c moves it up and down, and b slides the turning point. The roots, turning point and discriminant are worked out as you go.

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Questions students ask

What does the discriminant tell you?

b² − 4ac: if it is positive there are two real roots, if zero one repeated root, and if negative no real roots (the curve does not cross the x-axis).

How do you find the turning point of a quadratic?

x = −b/(2a); put that x back into the equation for y. It is a minimum when a > 0 and a maximum when a < 0.

Free notes on quadratic

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