write your answer in the form y = a(x - p)(x - q), where a, p, and q are integers, decimals, or simplified…

write your answer in the form y = a(x - p)(x - q), where a, p, and q are integers, decimals, or simplified fractions.

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: Identify p and q

Given x - intercepts (2,0) and (5,0), then $p = 2$ and $q = 5$. So the quadratic - function is in the form $y=a(x - 2)(x - 5)$.

Step2: Find the value of a

Substitute the point $(7,-3)$ into the equation $y=a(x - 2)(x - 5)$. We get $-3=a(7 - 2)(7 - 5)$. First, simplify the right - hand side: $(7 - 2)(7 - 5)=5\times2 = 10$. So the equation becomes $-3 = 10a$. Then solve for a: $a=-\frac{3}{10}$.

Answer:

$y =-\frac{3}{10}(x - 2)(x - 5)$