9514 1404 393
Answer:
y = -2x^2 +7x +4
Step-by-step explanation:
A graphing calculator or spreadsheet can tell you the quadratic regression formula that will fit these points:
y = -2x^2 +7x +4
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If you'd like to do this "by hand", you can substitute the given points into the equation y = ax^2 +bx +c to get three linear equations in a, b, c.
4 = 0 +0 +c
10 = a(2^2) +b(2) +c
0 = a(4^2) +b(4) +c
Using the value of c from the first equation, these reduce to ...
6 = 4a +2b
-4 = 16a +4b
Dividing the second of these equations by 2, and subtracting the first, we have ...
(16a +4b)/2 -(4a +2b) = (-4)/2 -(6)
4a = -8
a = -2
From the first of the reduced equations, we find ...
b = (6 -4a)/2 = 3 -2a = 3 -2(-2) = 7
So, a=-2, b=7, c=4, and the equation is ...
y = -2x^2 +7x +4
