Question

A convex parabola is shown in a coordinate plane. The parabola connects the points left-parenthesis negative 4.5 comma 12 right-parenthesis, left-parenthesis negative 3 comma 0 right-parenthesis, left-parenthesis 1 comma negative 12 right-parenthesis, left-parenthesis 4 comma 0 right-parenthesis, and left-parenthesis 6 comma 15 right-parenthesis.
Which of the following are the most likely factors of the function graphed above?

A. (x – 3)(x + 4)
B. (x + 3)(x – 4)
C. (x + 2)(x – 4)
D. (x)(x + 12)

Answer 1

Since the parabola is connecting the points, it means that the points given are on the parabola or that the points are solutions of the parabola. Thus, when we substitute the points into the function, we should end up with the correct y-value.

To find the correct choice, let's test a point. An easy point to test I believe would be (-3, 0) because we should be getting 0 as a y-value. Let's test:

$A. (- 3 - 3)(3 + 4) = -42$

$B. (-3 + 3)(-3 - 4) = 0$

$C. (-3 + 2)(-3 - 4) = 7$

$D. (-3)(-3 + 12) = -27$

We can see that Choice B is the correct function, because it produces 0 when we substitute $x = - 3$. Thus, Choice B, or (x + 3)(x - 4) is the answer.