Use Parts A and B as a model to draw a graph of what the satellite will look like.
A
a
4 feet
B
b
0.5 feet
C
c
y=1/6x^2-1.5
Practice makes perfect
a
To find how wide the satellite dish is, we can look at the graph that represents the cross section.
We can see that the satellite covers the space from x=- 2 to x=2. To find the width, we will subtract these values.
2-(- 2)=4
The satellite is 4 feet wide.
b
To find how deep the satellite dish is, we can look at the graph that represents the cross section.
We can see that the satellite ranges from y=- 0.5 to y=0. To find the satellite's depth, we can subtract these values.
0 - (-0.5)=0.5
The depth is 0.5 feet.
c
Now, we want to make a parabola that is 6 feet wide and 1.5 feet deep. This means that the domain of the parabola should be 6 feet and the range should be 1.5 feet. We also know that the x-axis represents the top of the satellite dish, so the graph must all be under the x-axis.
This graph is what we are trying to find. Notice that it has a vertex at ( 0, - 1.5), so we can use vertex form.
y=a(x- h)^2+ k ⇒ y=a(x- 0)^2+( - 1.5)
We also need to make sure that the parabola has x-intercepts at x=- 3 and x=3. To do this, we can substitute one of these points into our equation and solve for a.
