Question

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

Explanation:

Step1: Identify x - intercepts

The x - intercepts are $p=-5$ and $q = 3$, so the equation is $y=a(x + 5)(x - 3)$.

Step2: Find the value of a

Substitute the point $(1,6)$ into the equation: $6=a(1 + 5)(1 - 3)$. Then $6=a\times6\times(-2)$, so $a=-\frac{1}{2}$.

Answer:

$y=-\frac{1}{2}(x + 5)(x - 3)$