Question

Which of the following is the value of c for the best approximation for the quadratic function containing the points (5, 64), (7, 11), (9, -30), and (2, 4)?

A. -73
B. 50
C. -5
D. -17

Answer 1

There's some ambiguity in this question. Also, more points are given than are really necessary to fit a quadratic function as a best approximation.

Given that we want a quadratic model, I'd immediately write out

y=ax^2 + bx + c and then I'd assume that it is THIS c that we are supposed to find.

Please brainstorm on what to do next. How would we find a, b and c? Perhaps focusing on c alone would save you some time.

Answer 2

This problem is multi-step, by the way; you'll have to come up with 3 equations in 3 unknowns, namely, in a, b and c, and then you'll need to solve that system of linear equations, at least for c if not for a and b.

Answer 3

So, a quadratic equation looks like this

f(x) =k(x - a)(x-b)

We know that f(5)=64 and f(7) = 11 and f(2)=4

We have 3 equations and 3 unknowns. Solveable.

There are the 3 equations:

f(5)=64=k(5-a)(4-b)=k(20-5b-4a+ab)
f(7)=11=k(11-a)(11-b)=k(120-11b-11a+ab)
f(2)=4=k(2-a)(2-b)=k(4-2b-2a+ab)

So we now have

20k-4kb-4ak+abk=64
120k-11kb-11ka+kab=11
3k-2kb-2ka+kab=4

Make sense?

Answer 4

I your case, you are looking for kab.

Answer 5

Nice work, ybarrap.

An alternative approach would be to use the model y=ax^2 + bx + c.

Answer 6

@britneyspears