5.17: Using the Graphing Calculator to Graph Quadratic Equations
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
Guidance
A graphing calculator can be a very helpful tool when graphing parabolas. This concept outlines how to use the TI83/84 to graph and find certain points on a parabola.
Example A
Graph
Solution: Using a TI83/84, 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.
Example B
Using your graphing calculator, find the vertex of the parabola from Example A.
Solution: To find the vertex, press
Example C
Using your graphing calculator, find the
Solution: To find the
NOTE: 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.
Guided Practice
1. Graph
Answers
1. Using the steps above, the vertex is (0.917, 40.04) and is
Practice
Graph the quadratic equations using a graphing calculator. Find the vertex and

y=x2−x−6 
y=−x2+3x+28 
y=2x2+11x−40 
y=x2−6x+7 
y=x2+8x+13 
y=x2+6x+34 
y=10x2−13x−3 
y=−4x2+12x−3 
y=13(x−4)2+12 
y=−2(x+1)2−9  Calculator Investigation
 The
 parent graph
 of a quadratic equation is

y=x2  .
 Graph
y=x2,y=3x2 , andy=12x2 on the same set of axes in the calculator. Describe howa effects the shape of the parabola.  Graph
y=x2,y=−x2 , andy=−2x2 on the same set of axes in the calculator. Describe howa effects the shape of the parabola.  Graph
y=x2,y=(x−1)2 , andy=(x+4)2 on the same set of axes in the calculator. Describe howh effects the location of the parabola.  Graph
y=x2,y=x2+2 , andy=x2−5 on the same set of axes in the calculator. Describe howk effects 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 , wherex is the horizontal distance andy is the height (in feet) of the ball. Find the maximum height of the ball and its total distance travelled.
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Image Attributions
Here you'll use the graphing calculator to graph parabolas, find their intercepts, and the vertex.