Investigating: y = ax and y = ax + C 2

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Investigating: y = ax

2

and y = ax

2

+ C

* You can use a graphing calculator to explore the graph of a parabola. For this investigation, use a standard screen by pressing the ZOOM button then option 6.

1.) Graph these functions on the same screen. Then complete the statements below. y = x

2 y = 4x

2 y = 1/4x

2

(HINT: hit the TRACE button and use the arrow keys to move the cursor from 1 curve to the next to know which curve is which. The equation is in the upper left corner.)

* The graph of ___________________________ is closest to the y-axis. (Narrowest)

* The graph of ___________________________ is closest to the x-axis. (Widest)

2.) Graph the following function on the calculator and sketch them on the graph below.

Use a different color for each curve and label each. y = 1/2x

2 y = x

2 y = 2x

2

3.) Conjecture: Based on the graphs you analyzed in sections 1 and 2, make a conjecture regarding the relationship of the value of a and the wideness of the parabola.

4.) Graph the following equations on the same screen, Sketch them on the graph below in different colors and label each.

ANSWER: How does the sign of a affect the graph of the function? y = 6x

2 y = -6x

2

*Complete the statement: If the value of a is positive, the parabola opens

______________________

If the value of a is negative, the parabola opens

_____________________

5.) Graph the equations on individual screens. Write the coordinates of the vertex of each equation.

(HINT: Find the vertex by hitting 2

nd

TRACE, choose either Minimum or Maximum depending on the graph. Move cursor slightly left then ENTER, next slightly right then

ENTER; and ENTER again. The x and y values are your vertex.)

a.) y = x

2

+ 1 b.) y = x

2

- 2 c.) y = x

2

- 4 d.) y = x

2

+ 5

V=______________

V=_______________

V=_____________ V= ______________

Conjecture: Compare the vertices of each graph. Make a conjecture about the value of c and how it affects the graph.

6.) You can change the appearance of a graph by altering it’s scale in the WINDOW screen. Graph y = -2x

2

+ 1. Describe how the graph of y = -2x

2

+ 1 changes from it’s appearance on a standard screen when using different XMin, XMax, YMin, YMax values. a.) Hit WINDOW key. Change XMin to -5 and XMax to 5. Keep YMin at -10 b.) Hit WINDOW key. Change XMin to -10 and XMax to 10. Change YMin to -5

and YMax at 10.

How does this graph look different?

and YMax to 5.

How does this graph look different?

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