Quadratic in General form
A quadratic function is in GENERAL FORM if it is written as f(x)=ax2+bx+c
below is a function written in general form, with sliders for the a, b and c values.
By the end of this tutorial, you should understand:
how the a value affects the shape of the parabola
how the c value affects the shape of the parabola
Before you start, set your sliders so that the function is written as
Note: the on the end isn't needed, it's just
Investigating the "a" value
Click and drag the "a" value to the right. How does the parabola look when "a" equals 2? or 3? or 4 or 5? What does increasing the value of "a" do?
Drag the "a" value between 0 and 1. What does decreasing the "a" value, while keeping it positive, do to our parabola?
Drag the "a" value so that it is negative. How does this effect the shape of our parabola?
Investigating the c value.
Set your function to again.
Let's start from here and figure out what the c value does.
Try increasing the c value. What happens? Try decreasing the c value. What happens? Describe what you see
Now move the "a" value and the "b" value to different positions. Now move the "c" value? What particular point on the parabola does the "c" value always coincide with?
Summarise your findings
Complete these sentences:
In a quadratic in general form
The a value controls the _________________ of the function
As the a value increases ________________________________
as the a value decreases( but stays positive)_________________________________
When the a value becomes negative___________________________________
The c value controls ____________________________________
The c value always coincides with the ________________________________