What is the length of EF in the right triangle below? 25 7
1 answer:
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Answer:
Step-by-step explanation:
You have 3 unknowns: a, b, and c. It's our job to find them algebraically. I'm going to start with the point where x = 0 and y = 7. You'll see why in a minute. Filling in the standard form of a quadratic
using (0, 7):
gives you that c = 7. We will use that value now when we write the next 2 equations. Now the point (-2, 19):
and
so
12 = 4a - 2b
Now for the next point (-1, 12):
and
so
5 = a - b
Now we have a system of equations (the 2 bold font equations) that we will solve by elimination:
12 = 4a - 2b
5 = a - b
Multiply the bottom equation by -4 to get a new system:
12 = 4a - 2b
-20 = -4a + 4b
Add those together to get rid of the a terms and end up with
-8 = 2b so
b = -4
Now we can sub in -4 for b to solve for a. I'm using the second bold type equation to do this:
5 = a - (-4) and
5 = a + 4 so
a = 1 and the equation for the quadratic function is
Answer:
2nd graph (image)
Step-by-step explanation:
The function to graph is:
It follows the general pattern of the function: , which is general shape and in 1st and 3rd quadrants. So, we can eliminate 3rd and 4th choices (because of quadrants).
The answer is either 1st, or 2nd graph.
Now, we simply can check a point in both.
lets take x = 4, so the function would be:
f(4) = 4/4 = 1
Hence, point is:
(4,1)
The first graph doesn't go through this point. The second graph does.
hence, we can successfully choose the 2nd graph as our answer.