Activity
In an earlier lesson, we saw that an equation such as can model the height of an object thrown upward from a height of 10 feet with a vertical velocity of 78 feet per second.
1. Is the expression written in standard form? Be prepared to show your reasoning.
Compare your answer:
Yes. It is a sum of a squared term, a linear term, and a constant term. Written in the form , – 16 is , 78 is , and 10 is .
2. Paola said that the equation also defines the same function, written in factored form. Is Paola correct? Be prepared to show your reasoning.
Compare your answer:
Yes. Distribute the – 2 to and you have . Multiply this binomial by . The result of is .
3. Here is a graph representing both and .
a. What is the -value of the -intercept?
The -intercept is .
b. What is the -value of the -intercept?
The -intercept is .
c. What do each of these points mean in this situation?
Compare your answer:
The -intercept shows the height, in feet, of the object when it was thrown, and the -intercept shows the number of seconds that passed after the object was thrown before it hit the ground.
Self Check
Additional Resources
Characteristics of Quadratic Graphs
The graph of is shown below.
What are the - and -intercepts?
The -intercepts are where the graph crosses the -axis.
This happens at and .
The -intercept is where the graph crosses the -axis.
This happens at .
Try it
Try It: Characteristics of Quadratic Graphs
The graph of is below.
What are the - and -intercepts of the graph?
Compare your answer:
Here is how to find the intercepts:
For the -intercepts: Look at where the graph crosses the -axis.
This happens at and . So the points are and .
For the -intercept: Look at where the graph crosses the -axis.
This happens at so the point is .