Finding Polynomial Equations from Graphs

What are the zeros of the polynomial function?

• x = -2, x = 0, x = 3

• x = -2, x = 1, x = 3

• x = -1, x = 1, x = 2

• x = -3, x = 0, x = 2

What is the significance of the zeros in determining the polynomial function?

• They determine the slope of the graph.

• They indicate the maximum height of the graph.

• They are used to calculate the y-intercept.

• They are used to find the factors of the function.

How are the factors of the polynomial function related to its zeros?

• Factors are the sum of the zeros.

• Factors are x minus the zeros.

• Factors are the product of the zeros.

• Factors are x plus the zeros.

What does the 'multiplier' in a polynomial function represent?

• The highest degree of the polynomial

• The y-intercept of the graph

• A constant that scales the function

• The slope of the graph

Why was the initial attempt to find the multiplier using the y-intercept unsuccessful?

• It resulted in a division by zero.

• It led to an equation with infinite solutions.

• The y-intercept was not on the graph.

• The calculation was incorrect.

What does the y-intercept tell us about the polynomial function?

• The value of the multiplier

• The minimum value of the function

• The maximum value of the function

• It is used to find the value of the multiplier

Why is it important to find a new value of x and y when the initial attempt to find the multiplier fails?

• To resolve the issue of infinite solutions

• To avoid division by zero

• To correct a calculation error

• To simplify the equation

What value of x was used to successfully determine the multiplier?

• x = 0

• x = 1

• x = 2

• x = -1

What was the final value of the multiplier 'a'?

• a = 1

• a = 0

• a = 2

• a = -1

How is the final equation of the polynomial function expressed?

• f(x) = a(x^2 - 3x + 2)

• f(x) = (x + 2)(x - 3)

• f(x) = a(x - 2)(x + 3)

• f(x) = a(x + 2)(x)(x - 3)