write the equation of the parabola that passes through the points (1, 0), (6, 0), and (7, 30). write your…

write the equation of the parabola that passes through the points (1, 0), (6, 0), and (7, 30). write your answer in the form y = a(x - p)(x - q), where a, p, and q are integers, decimals, or simplified fractions.

write the equation of the parabola that passes through the points (1, 0), (6, 0), and (7, 30). write your answer in the form y = a(x - p)(x - q), where a, p, and q are integers, decimals, or simplified fractions.

Answer

Explanation:

Step1: Determine the form of the parabola

Since the parabola passes through ((1,0)) and ((6,0)), the equation of the parabola can be written in the form (y=a(x - 1)(x - 6)) (using the fact that if (y = a(x-p)(x - q)) and (y = 0) when (x=p) and (x = q)).

Step2: Substitute the third - point into the equation

Substitute (x = 7) and (y=30) into (y=a(x - 1)(x - 6)). We get (30=a(7 - 1)(7 - 6)). Simplify the right - hand side: (30=a\times6\times1), so (6a=30). Solve for (a): (a=\frac{30}{6}=5).

Answer:

(y = 5(x - 1)(x - 6))