Unit 4: Quadratics

4.1 Transformations on y = x²

Graph y = x², using a table of values. Note the relationship between different points.

To graph this parabola:

• plot the vertex coordinates (0, 0)

• go right 1, up 1; go left 1, up 1 for the next points
• go right 2, up 4; go left 2, up 4 from the vertex for the next points
• draw a smooth curve through the points.

This might be good enough for the basic parabola, but how does this change with transformations?

Ex 1 Graph without using a table of values.

(a) y = (x – 4)² (b) y = (x + 3)² – 2 (c) y = 2(x + 1)² + 4 (d) y = -3(x – 5)² – 2

To graph a parabola:

• plot the vertex coordinates (h, k)

• go right 1, up a; go left 1, up a for the next points
• go right 2, up 4a; go left 2, up 4a for the next points
• draw a smooth curve through the points

Ex 2 Given the graphs, state the equation for each in the form y = a(x – h)² + k

Homework Assignment