Math problem for school

Question

determine the coefficient of the x-term of the parabola that passes through the points (3,0), (9,0) and (14,77). use the formula y=a(x-p)(x-q) where p and q are the zeros to helo you to begin the problem. give your answer as a decimal and include the negative (indicating that the volume is decreasing)

Answer 1

Use the factor theorem, which states: The binomial (x - a) is a factor of the polynomial f(x) if and only if f(a) = 0. In other words, if "a" is a zero, then (x - a) is a factor of your polynomial. If your problem had included a factor "k" times, then you would have had the factor (x - a)^k in your polynomial equation.

y = a(x - 3)(x - 9)

We now have to adjust our equation for f(x) so that it passes through the given point. This will done by determining a value for the coefficient "a". Do this by plugging in the x and y values from the 3rd point that was given and then solving for "a".