Activity
Mai is learning to create computer animation by programming. In one part of her animation, she uses a quadratic function to model the path of the main character, an animated peanut, jumping over a wall.
Mai uses the equation to represent the path of the jump. represents the height of the peanut as a function of the horizontal distance it travels, .
On the screen, the base of the wall is located at , with the top of the wall at . The dashed curve in the picture shows the graph of one equation Mai tried, where the peanut fails to make it over the wall.
What is the value of in this equation?
.
What is the value of in this equation?
.
Starting with Mai's equation, choose values for and that will guarantee the peanut stays on the screen but also makes it over the wall. Be prepared to explain your reasoning.
Compare your answer:
- Use 22 for . Because is the -coordinate of the highest point of the jump, if that point is directly over the wall and the -value remains at 5, then the peanut would clear the wall. So the new equation would be .
- Change the value of , which is the vertical coordinate of the vertex, to 7 so that the vertex is at and there is still enough vertical distance to clear the 4.5-unit-tall wall when is 22. The new equation would be .
Video: Changing the Parameters of a Quadratic Expression
Watch the following video to learn more about changing the parameters of a quadratic expression.
Self Check
Additional Resources
Determining the Vertex From a Graph
Zaren made a paper football for a game at indoor recess and flicked it in the air from a table. The path of the paper football is shown below and represented by the function .
Find the value of the vertex and its meaning:
The peak of the graph is at . This means the maximum horizontal distance traveled was 17 inches when the height of the object was 3 inches.
Try it
Try It: Determining the Vertex From a Graph
The revenue made from a high school play is shown in the graph above. Find the vertex and tell what it means in this situation.
Here is how to find the vertex and determine its meaning:
The peak of the graph is at . This means that the maximum revenue is $1100 when the ticket price is $15.