Polynomial Functions Use the following information about the...

Polynomial Functions Use the following information about the graph of a polynomial function to determine the formula for the function • The y-intercept is (0, -48). • The x-intercepts are (-4, 0), (1, 0), and (4, 0). • Degree is 3. • End behavior: $f(x) \to \infty$ as $x \to -\infty$, and $f(x) \to -\infty$ as $x \to \infty$. f(x) =

Transcript

00:01 This problem wants us to determine what the polynomial or the polynomial function would be with the given characteristics of the y intercept being 018.

00:08 We have 2x intercepts of 3 .0 and negative 30.

00:11 We want the degree to be 2.

00:13 And we also want the end behavior to be correct where as x approaches infinity, in other words it goes to the right.

00:18 F of x, the y values go to negative infinity.

00:20 And the same thing as x approaches negative infinity or goes to the left, we want the y values to also approach negative infinity.

00:26 So we both, basically want both end behaviors to be falling on both ends or going down.

00:30 So to start, we're going to focus on the x intercepts to start building the polynomial because a 3 -0 solution would come from x minus 3 as a binomial, and negative 3 -0 as a solution would come from x plus 3 as a binomial.

00:44 So when we multiply these together, we get x squared plus 3x minus 3x, and negative 3 times negative 3, or negative 3 times positive 3 is negative 9.

00:55 So 3x minus 3x will eliminate, and we have x squared minus 9.

01:00 So this would be a function that is true for the x intercept so far at 30, negative 3 .0.

01:07 But one thing we need to worry about is what the y intercept is supposed to be.

01:10 We are supposed to be able to plug in 0 for x, and the result is supposed to be 18 after we evaluate.

01:17 But what happens when we plug in 0 for x is we get 0 squared, which is just 0, and 0 minus 9 is negative 9...

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