# Question below: Need explanation. I know how to do the work but I don't really understand it

The equation of the function h is h(x)=1/2(x-2)^2. The table shows some of the values of function m.

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x ¦ 8 ¦ 10 ¦ 12 ¦ 14 ¦

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m(x) ¦ 2 ¦ 3 ¦ 4 ¦ 5 ¦

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Part A: what is the value of h(4)-m(16)?

Part B: If both of these functions are graphed on the same coordinate plane, how far apart are the y-intercepts?

Part C: For what values of x does m(x) exceed h(x)

## 3 Answers By Expert Tutors

By: Tutor
4.7 (31)

Math and computer tutor/teacher

Thank you so much, I get way better now
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03/14/20

Tutor
New to Wyzant

UNC Grad Computer Science and Mathematics Tutor

Thank you. I didn't get why there are no values of m(x) that exceed h(x). But then it asks, for what values of x does m(x) exceed h(x). I used desmos, and I found the point (6, 7) is when the x values of m(x) exceed h(x).
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03/14/20

I dont get how the y-intercept is -2. I decided to use the pattern in the graph because it's linear, and I got 4. I saw how you got the y-intercept, and it seemed correct, but I don't get why the pattern I used didn't work.
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03/14/20

Tutor
New to Wyzant

Dedicated CS and Math Tutor

Hey, thank a lot for taking your time. The part I don't get, is part c. When I put both the equations into desmos, I found a point on function m that intersects with function h. I also found that the point (6, 7) was the point where m exceeds h. Of course, I could be wrong.
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03/14/20

I know that quadratic functions always exceed linear function, but when I look at the graph, it confuses me
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03/14/20

Elana E.

Hello! I'm sorry for my delay in responding, and also that I didn't look more carefully at part c when writing my first response. Actually, m(x) never exceeds h(x), and the two functions never intersect (perhaps check for typos in desmos?). Quadratic equations (at least those with positive coefficients of x^2) do eventually exceed linear functions. In this case, graphing the functions shows us that h is always greater than m. If you are not allowed to use a graphing calculator then you can use the quadratic formula, as Andrew T. suggested, to find that the functions do not intersect at any real point.
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03/16/20

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