Consider the table below.x    y-3  0.5-2  1-1  2.50  51  8.5y=ax2+bxComplete the standard form equation representing the quadratic relationship displayed above, where a, b, and c are constants.

Answer:   y = 0.5x² +3x +5Step-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 + c0.5 = 9a -3b +c . . . . first point1.0 = 4a -2b +c . . . . second point2.5 = a -b +c . . . . . . third pointSolving this system of equations by your favorite method gives ...   a = 0.5, b = 3, c = 5so the quadratic is ...   y = 0.5x² +3x +5__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 = 1That 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 +5Filling in x=1, we get   8.5 = 0.5 +b +5   3 = band the equation is ...   y = 0.5x² +3x +5__You can also let your graphing calculator or spreadsheet program show you a quadratic regression equation through these points. It gives the same result.