An arrow is shot straight up into the air from 5 feet above the ground with a velocity of 18 ft/s. The quadratic expression that represents this situation is
A graphing calculator can be a very helpful tool when graphing parabolas. This concept outlines how to use the TI-83/84 to graph and find certain points on a parabola.
Using a TI-83/84, press the
If your graph does not look like this one, there may be an issue with your window. Press ZOOM and then 6:ZStandard, ENTER. This should give you the standard window.
Using your graphing calculator, find the vertex of the parabola from Example A.
To find the vertex, press
Using your graphing calculator, find the
To find the
: When graphing parabolas and the vertex does not show up on the screen, you will need to zoom out. The calculator will not find the value(s) of any
Intro Problem Revisit
Use your calculator to find the vertex of the parabolic expression
The vertex is (0.5625, 10.0625). Therefore, the maximum height is reached at 0.5625 seconds and that maximum height is 10.0625 feet.
1. Using the steps above, the vertex is (-0.917, -40.04) and is
Graph the quadratic equations using a graphing calculator. Find the vertex and
of a quadratic equation is
y=x2,y=3x2, and y=12x2on the same set of axes in the calculator. Describe how aeffects the shape of the parabola.
y=x2,y=−x2, and y=−2x2on the same set of axes in the calculator. Describe how aeffects the shape of the parabola.
y=x2,y=(x−1)2, and y=(x+4)2on the same set of axes in the calculator. Describe how heffects the location of the parabola.
y=x2,y=x2+2, and y=x2−5on the same set of axes in the calculator. Describe how keffects the location of the parabola.
Real World Application
The path of a baseball hit by a bat follows a parabola. A batter hits a home run into the stands that can be modeled by the equation
y=−0.003x2+1.3x+4, where xis the horizontal distance and yis the height (in feet) of the ball. Find the maximum height of the ball and its total distance travelled.