STARTERSDraw a graph of: y = 3x – 2

Write the equation of the following graphs:

x = 2

y = -x + 1

STARTERSAn electrician charges $60 for calling and $45 per hour that he spends on the job.

Equation for the electrician charges =

Produce a graph of the charges

45H + 60

H C

0 60

1 105

2 150

3 195

4 240

5 285

STARTERSThe amount of oil O left in a leaky barrel after t minutes is given by the equation:

Produce a graph for the amount of oil left in the barrel

O = 160 – 5t

t O

0 160

2 150

4 140

6 130

8 120

10 110

A parabola has:

x2 as its highest power

The parabola is symmetric about the vertex

Note 3: Parabolas

Example: Draw the graph of y = x2

Investigate by plotting on your calculator

y = x2

y = x2 + 3 y = x2 - 1

Moving the Parabola Up/Down y = x2 + c

the vertex moves to c on the y-axis

Example: Plot y = x2 - 2

Investigate by plotting on your calculator

y = x2

y = (x + 1)2 y = (x – 2)2

Moving the Parabola Left/Right y = (x + a)2

the vertex moves to the opposite of a on the x-axis

Example: Plot y = (x + 4)2

Investigate by plotting on your calculator

y = x2

y = (x + 2)2 - 1 y = (x – 1)2 + 3

Moving the Parabola in both directions y = (x + a)2 + c

the vertex moves in both directions

Example: Plot y = (x - 2)2 - 3

Negative Parabolas y = -x2

the graph is reflected in the x-axis

Example: Plot y = -x2

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