The Expanded form and the Quadratic Formula
The value of a
Without moving the sliders for b and c, adjust a and observe how the curve changes. How does the value of a affect the curve?
The value of b
Keep the value of a = 1 and c = 0. Move the slider for b and observe how the curve changes. How does the value of b affect the curve?
The value of c
Keep the value of a = 1 and b = -2. Move the slider for b and observe how the curve changes. How does the value of c affect the curve?
Roots
Move the sliders to change the values of a, b and c. What are the minimum and maximum number of roots for a quadratic?
Roots
The Quadratic formula: (Tick both boxes in the applet) The quadratic formula gives the roots of a quadratic equation. Move the sliders to change the values of a, b and c. Now compare the answers of the formula to the points on the curve. What do you notice?
Repeated roots
Give an example of a quadratic expression that results in "two repeated roots". Try to factorise the expression.
No real roots
What happens to the calculation for the quadratic formula when there are "no real roots"?