Question

Which equation could represent each grapes polynomial function?

Answer 1

1. y=(x+4)(x-1)(x-4)

2. y=(x+6)(x+1)(x-2)(x-8)

Explanation:

The first graph shows a cubic function with three x-intercepts at (-4,0), (1,0) and (4,0). So, the zeros of the function are -4, 1, and 4. Rewriting each zero, m, as a factor in the form (x − m) gives the factors for the polynomial: (x + 4), (x − 1), and (x − 4). So, an equation for the function could be y = (x + 4)(x − 1)(x − 4).The graph of the quartic function has x-intercepts at (-6,0), (-1,0), (2,0), and (8,0). The zeros of this function are -6, -1, 2, and 8. So, the factors of the function are (x + 6), (x + 1), (x − 2), and (x − 8). The equation y = (x + 6)(x + 1)(x − 2)(x − 8) could represent the function.

Answer 2

9514 1404 393

Answer:

• top graph: y = x(x +3)(x -2)
• bottom graph: y = x⁴ -5x² +4

Explanation:

Each x-intercept at x=a corresponds to a polynomial factor of (x -a).

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The top graph has x-intercepts of -3, 0, +2, so the factors of this cubic are ...

y = (x +3)(x -0)(x -2)

y = x(x +3)(x -2) . . . . . . . matches upper right tile

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The bottom graph has x-intercepts of -2, -1, 1, 2, so the factors of this quartic are ...

y = (x +2)(x +1)(x -1)(x -2) = (x² -4)(x² -1)

y = x⁴ -5x² +4 . . . . . . . matches lower left tile