Answer:
y = (1/2)(x + 4)(x + 1)(x - 3)
Step-by-step explanation:
Since this graph begins in Quadrant III and continues growing in Quadrant I, and has three roots/zeros, we know immediately that it's a cubing function and can confidently write out
y = d(x - a)(x - b)(x - c) as one general form of the cubing function.
In this particular case we have:
y = d(x + 4)(x + 1)(x - 3) (where the '4' comes from the x-intercept (-4, 0) )
From the graph we know that y = -6 when x = 0, and therefore:
-6 = d(0 + 4)(0 + 1)(0 - 3), or -6 = d(-12), leading to d = 1/2
Then our tentative equation (above) becomes y = (1/2)(x + 4)(x + 1)(x - 3)
