Introduction to Parabolas
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.
