2
2
* 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?