Question

Consider the table below.

Answer 1

Answer:

  y = 0.5x² +3x +5

Step-by-step explanation:

There are several ways to do this. The most straightforward may be to fill three table values into the equation and solve for a, b, c. Using the first three values, the equations would be ...

  y = ax² + bx + c

• 0.5 = 9a -3b +c . . . . first point
• 1.0 = 4a -2b +c . . . . second point
• 2.5 = a -b +c . . . . . . third point

Solving this system of equations by your favorite method gives ...

  a = 0.5, b = 3, c = 5

so the quadratic is ...

  y = 0.5x² +3x +5

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Since you are given the y-intercept (0, 5), you know the constant in the equation is 5. The given table values are equally-spaced, so finding differences can be informative.

  first differences: 1 -0.5 = 0.5; 2.5 -1 = 1.5; 5 -2.5 = 2.5; 8.5 -5 = 3.5

  second differences: 1.5 -0.5 = 1; 2.5 -1.5 = 1; 3.5 -2.5 = 1

That is, second differences are 1, which value is double the "a" coefficient of the equation. So, we know the equation is ...

  y = 0.5x² +bx +5

Filling in x=1, we get

  8.5 = 0.5 +b +5

  3 = b

and the equation is ...

  y = 0.5x² +3x +5

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You can also let your graphing calculator or spreadsheet program show you a quadratic regression equation through these points. It gives the same result.