I know how to graph polynomial functions, but i'm having a hard time getting the second point on this one.
f(x)=x(x-1)(x+2)(x+2).
I graphed my zeros and made the right arrow go up and the left arrow go down. I plotted my first point by pluggin in -1. My first point is (-1,2). On my answer sheet there is a point at (1,-1.5). How do i know that i need to solve for another point? And how to i get the point (1, -1.5)?
highest x power is x^4, even, always + so
as x gets big -, f gets big +
as x gets big +, f gets big +
so I do not understand your little arrow on the left.
Now as far as I know, f(x) is 0 at x = 1, so there is no point at (1,-1.5)
however guessing what might be intended if x = -1.5, f(-1.5) =
(-1.5)(-2.5)(.5)(.5)
= .9375
oh well, I do not know why you see that point in the answer.
there is a point and actually the point is (.5,-1.5). Would that make more sense? Thanks for your help
well, try that point
f(.5) = .5*-.5*2.5*2.5 = -1.56
so I get
(.5, -1.56)
To find the point (1, -1.5) for the polynomial function f(x) = x(x-1)(x+2)(x+2), you need to solve for the y-coordinate by plugging in x = 1 into the function.
Step 1: Start with the polynomial function f(x) = x(x-1)(x+2)(x+2).
Step 2: Substitute x = 1 into the function and evaluate: f(1) = 1(1-1)(1+2)(1+2).
Step 3: Simplify the expression: f(1) = 1(0)(3)(3) = 0.
The y-coordinate of the point (1, -1.5) is -1.5, but the function evaluated at x=1 gives a value of 0. Therefore, (1, -1.5) is not a point on the graph of f(x).
It seems like there may be a mistake in the answer sheet. The correct point you need to find depends on the context of the problem or any specific instructions given. If you need to find additional points on the graph, you can choose any x-value other than -1 and 1 and evaluate f(x) to find the corresponding y-coordinate.