Question

which equation could represent each graphed polynomial function? drag the tiles to the correct boxes. not all tiles will be used. pairs two graphs tiles $y = (x + 6)(x + 1)(x - 2)(x - 8)$ $y = (x - 4)(x + 1)(x + 4)$ $y = (x + 4)(x - 1)(x - 4)$ $y = (x - 6)(x - 1)(x + 2)(x + 8)$

Explanation:

Step1: Identify roots of first graph

The first graph crosses the x-axis at $x=-4$, $x=1$, $x=4$. These are the roots, so the factors are $(x+4)$, $(x-1)$, $(x-4)$.

Step2: Match to tile equation

The equation with these factors is $y=(x+4)(x-1)(x-4)$.

Step3: Identify roots of second graph

The second graph crosses the x-axis at $x=-6$, $x=-1$, $x=2$, $x=8$. These are the roots, so the factors are $(x+6)$, $(x+1)$, $(x-2)$, $(x-8)$.

Step4: Match to tile equation

The equation with these factors is $y=(x+6)(x+1)(x-2)(x-8)$.

Answer:

Top graph (with roots at -4, 1, 4): $\boldsymbol{y=(x+4)(x-1)(x-4)}$
Bottom graph (with roots at -6, -1, 2, 8): $\boldsymbol{y=(x+6)(x+1)(x-2)(x-8)}$