write the equation of the parabola shown in the graph. write your answer in the form y = a(x - p)(x - q)…

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.

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.

Answer

Explanation:

Step1: Identify the x - intercepts

The x - intercepts are $x=-1$ and $x = 3$. So, $p=-1$ and $q = 3$ in the factored form $y=a(x - p)(x - q)$. The equation becomes $y=a(x + 1)(x - 3)$.

Step2: Substitute a point to find a

We know the parabola passes through the point $(2,6)$. Substitute $x = 2$ and $y=6$ into $y=a(x + 1)(x - 3)$: $6=a(2 + 1)(2 - 3)$ $6=a(3)(-1)$ $6=-3a$ Solve for $a$: $a=-2$.

Answer:

$y=-2(x + 1)(x - 3)$