Question

use for question 13

1. what is the most likely equation for the graph above?

use for question 14
a. ( y = (x - 3)(x + 1) )
b. ( y = (x + 3)(x - 1) )
c. ( y = - (x - 3)(x + 1) )
d. ( y = - (x + 3)(x - 1) )

Explanation:

Step1: Identify x-intercepts

The graph crosses the x-axis at $x=3$ and $x=-1$. For a quadratic equation in factored form $y=a(x-r_1)(x-r_2)$, $r_1$ and $r_2$ are the x-intercepts. So the equation has factors $(x-3)$ and $(x+1)$.

Step2: Determine leading coefficient sign

The parabola opens downward, so the leading coefficient $a$ is negative.

Step3: Match to options

Combining these, the equation is $y=-(x-3)(x+1)$, which matches option c.

Answer:

c. $y = - (x - 3)(x + 1)$