Families of Parabolas

Share the samevertex

Share the axisofsymmetry

Have the Same Shape

Graph each group of equations on the same screen.Compare and contrast the graphs.What conclusions can be drawn? y = x2

y = 0.2x2

y = 3x2

Your graph should look like thisy = 3x2

y = x2

y = 0.2x2

Graph each group of equations on the same screen.Compare and contrast the graphs.What conclusions can be drawn?

y = x2

y = x2-6

y =x2+3

Your graph should look like this

y = x2-6

y=x2+3

y = x2

Graph each group of equations on the same screen.Compare and contrast the graphs.What conclusions can be drawn? y = x2

y = (x + 2)2

y = (x -4)2

Your graph should look like this

y=(x-4)2

y=x2

y = (x+2)2

Graph each group of equations on the same screen.Compare and contrast the graphs.What conclusions can be drawn?

y = x2

y = (x-7)2+2

Your graph should look like this

Your Turn

Graph each group of equations on the same screen.Compare and contrast the graphs.What conclusions can be drawn?

y = x2

y = 2x2

y= 4x2

Your Turn

Graph each group of equations on the same screen.Compare and contrast the graphs.What conclusions can be drawn?

y = x2

y = x2 -1

y= x2 -8

Your Turn

Graph each group of equations on the same screen.Compare and contrast the graphs.What conclusions can be drawn?

y = x2

y = -x2

Graph each group of equations on the same screen.Compare and contrast the graphs.What conclusions can be drawn?

y = -x2

y = -(x+2)2

y = -(x+4)2

General Rules For Shifts in Parabolas

The parent parabola is y = x2

1. For y = a x2

– if a is positive the parabola will open upward – if a is negative the parabola will open downward – as a increase in absolute value the parabola gets

more narrow

2. For y = (x+b)2 shifts the graph to the left b units For y = (x-b)2 shifts the graph to the right b units

General Rules for

3. For y = x2 +c shifts the graph upward b units For y = x2 -c shifts the graph downward b units

4. You can have a combination of shiftsy = (x + b)2 –c will shift the graph of y = x2 b units

to the left and c units downward

One Last ProblemIn a computer game, a player dodges spaced shuttles that are

shaped like parabolas. Suppose the vertex of one shuttle is at the origin. The shuttle’s initial shape and position are given by the equation y = 0.5x2. It leaves the screen with its vertex at (6,5).

Find an equation to model the final shape of the shuttle.

HOMEWORK

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