Final answer:
The formula for a parabola with horizontal intercepts and a given point can be found using the standard form of a quadratic equation and substituting the coordinates of the point and the roots into the equation.
Step-by-step explanation:
The formula for a parabola (quadratic function) with horizontal intercepts (roots) at x=9.9 and x=8.7 and passing through the point (0, 8.5) can be defined using the standard form of a quadratic equation, which is y = ax^2 + bx + c. To find the values of a, b, and c, we can substitute the coordinates of the point and the roots into the equation.
Substituting point (0, 8.5) into the equation, we get 8.5 = a(0)^2 + b(0) + c, which simplifies to c = 8.5.
Substituting the roots x=9.9 and x=8.7 into the equation, we get 0 = a(9.9)^2 + b(9.9) + 8.5 and 0 = a(8.7)^2 + b(8.7) + 8.5. These two equations can be solved to find the values of a and b, and the resulting equation will give the formula for the parabola.