Question

question 3 of 10
which of the following functions best describes this graph?
a. $y = (x + 5)(x - 4)$
b. $y = (x - 3)(x - 6)$
c. $y = x^2 - 2x + 4$
d. $y = x^2 + 9x + 18$

Explanation:

Step1: Find x-intercepts from graph

The parabola crosses the x-axis at $x=-5$ and $x=4$. These correspond to factors $(x+5)$ and $(x-4)$.

Step2: Match to factored function

A quadratic function with roots $r_1$ and $r_2$ has the form $y=(x-r_1)(x-r_2)$. Substituting $r_1=-5$ and $r_2=4$ gives $y=(x+5)(x-4)$.

Step3: Verify other options (optional)

• Option B: Roots at $x=3,6$ (right of y-axis, does not match graph)
• Option C: Discriminant $\Delta=(-2)^2-4(1)(4)=-12<0$, no real x-intercepts (does not match)
• Option D: Roots at $x=\frac{-9\pm\sqrt{81-72}}{2}=-3,-6$ (both left of y-axis, does not match)

Answer:

A. $y=(x+5)(x-4)$