Happy Mathematical Families
Mr Quadratic is a family man. His mathematical name is y = x2 or f(x) = x2.
Using desmos.com type in his name and have a look at his shape.
Mrs Quadratic is called y = x2 + 1 and their children are y = x2 + 2, y = x2 + 3, y = x2 – 1 and y = x2 – 2
1.
Draw this family and describe what you notice.
Their cousins, Mr and Mrs Negative also have mathematical names.
They are y = -x2 and y = -x2 + 1, and their children are y = -x2 + 2, y = -x2 + 3, y = -x2 - 1 and y = -x2 -2
2.
Draw these in the same way and describe this family.
Mr and Mrs Quadratic have neighbours who have mathematical names of y = 2x2 and y = 2x2 + 1, and their
children are y = 2x2 + 2, y = 2x2 – 1, y = 2x2 – 2 and y = 2x2 - 3
3.
Draw these in the same way and describe this family.
4.
What does the coefficient of x2 (the number before the x2) do to the graph?
5.
What does the constant on the end do to the graph?
6.
In your book draw up two sets of axes from -6 to 12 on the vertical (y) axis and -3 to 3 on the horizontal (x)
axis, then plot the following.
a.
y = x 2+ 4
y = x2 + 5
y = x2 - 3
y = x2 - 4
b.
y = -x2 + 4
y = -x2 + 5
y = -x2 - 3
y = -x2 - 4
Use your device to check that you have done them correctly.