Answer:
Step-by-step explanation:
If you plot the vertex and the point that it goes through, the point it goes through is above the vertex, so the vertex is a positive one that opens upwards. The general vertex form of a parabola of this type is
We have the x, y, h, and k. We will plug all those in and solve for a. That looks like this:
which simplifies to
-5 = 4a - 13 and
8 = 4a so
a = 2
That means that the paraobola in vertex form is
Answer:
The length of the wire is 15 ft.
Step-by-step explanation:
The solution of this exercise comes from an application of the Pythagorean theorem. The explanation here is complemented with the figure attached.
In the figure the segments AB and CD represents the vertical poles, where the length of AB is 6 ft and the length of CD is 15 ft. We want to find the length of the segment BD, that represents the stretched wire. The length of the segment AC is 12 ft, which is the distance between the poles.
If we draw an imaginary line from A perpendicular to DC, we obtain a rectangle ABEC, and a right triangle BED. Then, the length of BE is 12 ft. Moreover, the length of CE is 6 ft, because is equal to the length of AB. Hence, the length of DE is 9 ft, because DE = DC-EC.
As we want to find the length of the hypotenuse BD of the right triangle BED, and we already have the lengths of the other two sides, we only need to apply the Pythagorean theorem. This is
Then, taking square roots in both sides: BD=15 ft.
