Question

Find a quadratic function that includes the set of values below.

Answer 1

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