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Find a quadratic function that includes the set of values below.
(0,4), (2,8), (3,1)

1 Answer

5 votes

Answer:

y = -3x² +8x +4

Explanation:

You want a quadratic function that includes the points (0,4), (2,8), (3,1).

Quadratic regression

The coefficients are easily found using the quadratic regression function of a graphing calculator. The one in the attachment tells us the quadratic is ...

y = -3x² +8x +4

Equations

If you'd rather do this "by hand", you can presume a form for the function, then solve the resulting equations for the necessary coefficients.

We want the coefficients a, b, c for the equation ...

y = ax² +bx +c

point (0, 4): 4 = a(0²) +b(0) +c ⇒ c = 4

point (2, 8): 8 = a(2²) +b(2) +4 ⇒ 2a +b = 2 . . . subtract 4, divide by 2

point (3, 1): 1 = a(3²) +b(3) +4 ⇒ 3a +b = -1 . . . subtract 4, divide by 3

Solution

Subtracting the second equation from the third, we have ...

(3a +b) -(2a +b) = (-1) -(2)

a = -3 . . . . . . . simplify

Substituting for 'a' in the second equation gives ...

2(-3) +b = 2

b = 8 . . . . . . . . add 6

Now we have a=-3, b=8, c=4 and the quadratic is ...

y = -3x² +8x +4

Find a quadratic function that includes the set of values below. (0,4), (2,8), (3,1)-example-1
User Shunty
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