Algebra Polynomial Functions Quiz

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Questions and Answers

What is the value of the y-intercept for the function f(x) = -2(5x + 1)²?

  • -2 (correct)
  • 5
  • 0
  • 1

What expression can be used to find the y-intercept of the function f(x) = 6x + 6 + 2x³ - 8x²?

  • 6(2) + 6
  • 6(-2) + 6
  • 2(0)³ + 6
  • 6(0) + 6 + 2(0)³ - 8(0)² (correct)

After substituting x = 0 in the function f(x) = 6x + 6 + 2x³ - 8x², what is the value of f(0)?

  • 6 (correct)
  • 12
  • 2
  • 0

What are the real solutions of the equation $f(x) = 0$?

<p>0, -3, -2 (C)</p> Signup and view all the answers

Which of the following points represents a root of the function $f(x)$?

<p>(0, 0) (B)</p> Signup and view all the answers

What is the result of f(0) for the function f(x) = -2(5x + 1)²?

<p>-2 (D)</p> Signup and view all the answers

What is the factored form of the function represented in the graph?

<p>$f(x) = x(x+3)(x+2)$ (C)</p> Signup and view all the answers

Which step is NOT involved in finding the y-intercept of the function f(x) = 6x + 6 + 2x³ - 8x²?

<p>Factoring the polynomial (C)</p> Signup and view all the answers

At what x-value does the function $f(x)$ first intersect the x-axis?

<p>-3 (B)</p> Signup and view all the answers

How many real solutions does the equation $f(x) = 0$ have?

<p>3 (C)</p> Signup and view all the answers

What is the leading term of the polynomial function f(x) = x4 - 10x3 + 5x2 + 10x + 6?

<p>x4 (B)</p> Signup and view all the answers

What is the leading coefficient of the polynomial function f(x) = x4 - 10x3 + 5x2 + 10x + 6?

<p>1 (A)</p> Signup and view all the answers

What is the degree of the polynomial function f(x) = x4 - 10x3 + 5x2 + 10x + 6?

<p>4 (C)</p> Signup and view all the answers

Which term in the polynomial f(x) = x4 - 10x3 + 5x2 + 10x + 6 has the highest power?

<p>x4 (B)</p> Signup and view all the answers

Which of the following statements is true about the polynomial f(x) = x4 - 10x3 + 5x2 + 10x + 6?

<p>It has a leading coefficient of 1. (B)</p> Signup and view all the answers

Flashcards

What is the y-intercept?

The y-intercept is the point where a function's graph crosses the y-axis. It occurs when x = 0.

Finding y-intercept for factored functions

To find the y-intercept of a factored function, simply substitute x = 0 into the function and solve for f(x).

Finding y-intercept for unfactored functions

To find the y-intercept of an unfactored function, simply substitute x = 0 into the function and solve for f(x).

First step to finding the y-intercept

The first step to finding the y-intercept of any function is to substitute x = 0 into the function.

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Finding the y-intercept

The y-intercept can be found by substituting x = 0 into the function.

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X-intercepts

The points where the graph of a function crosses the x-axis.

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Roots of a function

The values of x where the function equals zero (f(x) = 0).

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Finding roots from a graph

The process of finding the roots or solutions of a function by examining its graph.

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Relationship between intercepts and solutions

The solutions of a function are represented by the x-values where the graph intercepts the x-axis.

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Factored form of a function

A factored form of the function that shows the relationship between the roots and the function.

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Leading Term

The term with the highest power of 'x' in a polynomial function.

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Leading Coefficient

The numerical coefficient of the Leading Term.

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Degree of a Polynomial

The highest power of 'x' in a polynomial function.

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