Question

98 points and branliest! I need help bad. These questions are all based on the graph. I would even appreciate some of the questions being answered.
What are the standard form and the factored form of the function?

What are the zeros of the function?

Part D
Use the zeros to find all of the linear factors of the polynomial function.

Write the equation of the graphed function f(x), where a is the leading coefficient. Use the factors found in part D. Express the function as the product of its leading coefficient and the expanded form of the equation in standard form.

Use the y-intercept of the graph and your equation from part E to calculate the value of a.

Part G
Given what you found in all of the previous parts, write the equation for the function shown in the graph.

Plot the graph of the function you wrote in part G.

Answer 1

Answer:

  see below

Step-by-step explanation:

C. The zeros can be read from the x-intercepts of the graph.

The zeros are -20, -5, +15.

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D. For zero "p", a linear factor will be (x -p). The linear factors are ...

  (x +20), (x +5), (x -15)

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B. The factored form of the function is ...

  f(x) = a(x +20)(x +5)(x -15) . . . . . for some scale factor "a"

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E. The standard form of the function will be the multiplied-out version of the factored form:

  f(x) = a(x^3 +10x^2 -275x -1500)

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A. Using the distributive property, the full expanded standard form is ...

  f(x) = ax^3 +10ax^2 -275ax -1500a

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F. The graph shows the y-intercept to be y=1. The function of parts E and/or A show the constant to be -1500a, so we have ...

  -1500a = 1

  a = -1/1500

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G. The graphed function is ...

  f(x) = (-1/1500)(x^3 +10x^2 -275x -1500)

See the attachment for a graph.

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Disclaimer

We have tried to decipher the question's parts and to put them in an order corresponding to the way the problem is actually solved. It isn't clear exactly how "multiplied-out" the function is supposed to be at any stage. We have chosen to avoid having fractional coefficients, which may not be what you are expected to do.