Introduction to Parabolas
While the graph of a linear equation is a straight line, the graph of a quadratic equation is a curve called a parabola. Parabolas are more complicated to graph than lines, but they have distinct features and properties that you can use to help with graphing. This lecture series explores what all parabolas have in common and how to use them to model real-life situations. Watch the videos and complete the interactive exercises.
Interpret parabolas in context
Answers
1.
Which feature?
Let's think about what each feature of a parabola shows about the function it represents:
| Feature | What it shows |
|---|---|
| \(x\)-intercept | The input(s) that produce an output of \(0\) |
| \(y\)-intercept | The output when the input is \(0\) |
| Vertex | The smallest or largest possible output and the corresponding input |
Which feature corresponds to when there are no more bacteria in the population?
The \(x\)-intercept \((4,0)\) shows that at \(4\) days, the population size is \(0\).
Answer
The \(x\)-intercept \((4,0)\) corresponds to when there are no more bacteria in the population.
2.
Which feature?
Let's think about what each feature of a parabola shows about the function it represents:
| Feature | What it shows |
|---|---|
| \(x\)-intercept | The input(s) that produce an output of \(0\) |
| \(y\)-intercept | The output when the input is \(0\) |
| Vertex | The smallest or largest possible output and the corresponding input |
Which feature corresponds to the bird's height above the ground when it jumped?
The \(y\)-intercept shows that at the moment the bird jumped, it was \(12\) meters above the ground.
Answer
The \(y\)-intercept \((0,12)\) corresponds to the bird's height above the ground when it jumped.
3.
Which feature?
Let's think about what each feature of a parabola shows about the function it represents:
| Feature | What it shows |
|---|---|
| \(x\)-intercept | The input(s) that produce an output of \(0\) |
| \(y\)-intercept | The output when the input is \(0\) |
| Vertex | The smallest or largest possible output and the corresponding input |
Which feature corresponds to the ball's maximum height?
The vertex shows that \(4\) seconds after Cassie hit it, the ball reached a maximum height of \(80\) meters above the ground.
Answer
The vertex \((4,80)\) corresponds to the ball's maximum height.
4.
Which feature?
Let's think about what each feature of a parabola shows about the function it represents:
| Feature | What it shows |
|---|---|
| \(x\)-intercept | The input(s) that produce an output of \(0\) |
| \(y\)-intercept | The output when the input is \(0\) |
| Vertex | The smallest or largest possible output and the corresponding input |
Which feature corresponds to when the ball hit the ground?
The \(x\)-intercept \((4,0)\) shows that \(4\) seconds after Mia kicked it, the ball is 000 meters above the ground.
Answer
The \(x\)-intercept \((4,0)\) corresponds to when the ball hit the ground.
