Question

Please help i thought this was a helping wbsite but been tryingto help help for days and nobody has responded to anything

Answer 1

Esmeralda and Heinz both work in a science lab. In order to secure funding for their future experiments, they must present their findings to some investors. The investors are not interested in listening to formulas. They want to see graphs because they are visual people. Unfortunately, Esmeralda and Heinz are having some difficulties.

Esmeralda and Heinz are working to graph a polynomial function, f(x). Esmeralda says that the third-degree polynomial has four intercepts. Heinz argues that the function only crosses the x-axis three times. Is there a way for them both to be correct? Explain your answer.

Heinz has a list of possible functions. Pick one of the g(x) functions below, show how to find the zeros, and then describe to Heinz the other key features of g(x).
g(x) = x3 – x2 – 4x + 4
g(x) = x3 + 2x2 – 9x – 18
g(x) = x3 – 3x2 – 4x + 12
g(x) = x3 + 2x2 – 25x – 50
g(x) = 2x3 + 14x2 – 2x – 14

Provide a rough sketch of g(x). Label or identify the key features on the graph.

Esmeralda is graphing a polynomial function as a parabola. Before she begins graphing it, explain how to find the vertex. Make sure you include how to determine if it will be a maximum or minimum point. Use an example quadratic function to help you explain and provide its graph.

Heinz boasts that he can predict the degree of a polynomial function just by looking at the end behavior. Can Heinz do this? Explain.

Answer 2

Usually long problems like this scares people away. I don't blame them to be honest.

Anyways, for the part

"Esmeralda and Heinz are working to graph a polynomial function, f(x). Esmeralda says that the third-degree polynomial has four intercepts. Heinz argues that the function only crosses the x-axis three times. Is there a way for them both to be correct? Explain your answer."

the basic idea is this: a third degree polynomial has at most 3 roots due to the fundamental theorem of algebra. So saying it has 4 x-intercepts is incorrect. However, if you mean "intercepts" as in x and y intercepts, then you could have 3 x-intercepts and 1 y intercept. So it's possible with that interpretation.

Answer 3

i finished it already .... but i seriously need help on other stuff.

Answer 4

I'll do one more part and leave the rest for you.


Find the roots of g(x) = x^3 – x^2 – 4x + 4


we set x^3 – x^2 – 4x + 4 equal to zero and solve for x. We will factor by grouping.


x^3 – x^2 – 4x + 4 = 0

(x^3 – x^2) + (-4x + 4) = 0

x^2(x – 1) + (-4x + 4) = 0

x^2(x – 1) - 4(x - 1) = 0

(x^2 - 4)(x-1) = 0

(x-2)(x+2)(x-1) = 0

x-2=0, x+2=0, x-1=0

x=2, x=-2,x=1


The three roots are x=2, x=-2,x=1

Answer 5

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