Algebra II Review - Units 1 & 2
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Questions and Answers

Which of the following is NOT a zero of $f(x) = 2x^3 - 5x^2 - 14x + 8$ given $f(4) = 0$?

  • 4
  • -2
  • 8 (correct)
  • 2
  • What is the sum of $a$, $b$, and $c$ when $2x^4 - x^3 + 4$ is divided by $x + 1$ yielding the expression $2x^3 - 3x^2 + ax + b + x + 1$?

  • 7 (correct)
  • 1
  • -1
  • 13
  • How many zeros, with multiplicities, does the equation $f(x) = x^2(x + 6)(x - 1)^2$ have?

  • 6
  • 3
  • 4
  • 5 (correct)
  • If $h(-2) = 0$, which of the following is NOT true?

    <p>h(x) has a factor of $(x - 2)$ (C)</p> Signup and view all the answers

    Which function could represent $g(x)$ based on the given graph?

    <p>$g(x) = x^2(x + 2)^2(x - 1)^2$ (C)</p> Signup and view all the answers

    If $(x + 5)$ is a factor of the polynomial $p(x) = x^3 - 2x^2 - 23x + 60$, which of the following represents the other factors?

    <p>$(x + 4)(x + 3)$ (B)</p> Signup and view all the answers

    If $x = -6$ is a root of $f(x) = x^3 + 6x^2 + 5x + 30$, which of the following is also a root of $f(x)$?

    <p>$x = -5$ (A)</p> Signup and view all the answers

    Which statement is FALSE based on the provided graph?

    <p>The graph crosses the x-axis at two points. (C)</p> Signup and view all the answers

    What is the y-intercept of the quadratic function $y = 2(x - 2)^2 + 2$?

    <p>(0, -6) (C)</p> Signup and view all the answers

    Which quadratic function has the wider graph?

    <p>$y = -2x^2$ (A)</p> Signup and view all the answers

    What are the solutions to the quadratic equation $x^2 - 6x = -15$?

    <p>$3 pm rac{i}{ rac{ extcolor{red}{5}}{ extcolor{red}{3}}} \sqrt{6}$ (C)</p> Signup and view all the answers

    Under what condition does the equation $ax^2 - bx = 0$ imply that $x = 0$ is a solution?

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

    How do you rewrite the quadratic function $y = -x^2 - 8x - 7$ in vertex form?

    <p>$y = -(x + 4)^2 - 7$ (D)</p> Signup and view all the answers

    What is the value of the discriminant for the quadratic function $y = 2x^2 - 3x + 5$ and what does it indicate?

    <p>-4, no real roots (B)</p> Signup and view all the answers

    What are the remaining zeros of the polynomial $f(x) = 7x^3 - 33x^2 + 15x + 20$ given that $x = 4$ is a zero?

    <p>1, 2 (D)</p> Signup and view all the answers

    What is the result of multiplying the binomials $(2x - 3)(3x + 2)$?

    <p>$6x^2 + 2x - 9$ (A)</p> Signup and view all the answers

    What is the solution to the inequality $2|x + 3| > 6$ written in interval notation?

    <p>(-∞, -6) ∪ (0, ∞) (B)</p> Signup and view all the answers

    What is the correct quadratic function $f(x)$ that intersects the x-axis at the points $(-3, 0)$ and $(5, 0)$ and has a point $(1, -32)$?

    <p>$f(x) = -2(x - 3)(x + 5)$ (C)</p> Signup and view all the answers

    Which equation represents the axis of symmetry for the parabola that passes through the points $(-4, 0)$ and $(6, 0)$?

    <p>$x = 2$ (B)</p> Signup and view all the answers

    What is the equation of the line in slope-intercept form that goes through the point $(-4, 2)$ and is perpendicular to the line $y = -\frac{1}{3}x + 2$?

    <p>$y = 3x - 10$ (B)</p> Signup and view all the answers

    Which quadratic function has a minimum value of -4 and an axis of symmetry at $x = 2$?

    <p>$f(x) = (x - 2)^2 - 4$ (D)</p> Signup and view all the answers

    Which representation corresponds to the quadratic function $y = -2(x + 2)(x - 1)$?

    <p>$y = -2x^2 - 2x + 4$ (B)</p> Signup and view all the answers

    What is the product of the solutions to the system of equations $3x - y + 5 = 0$ and $2x + 3y - 4 = 0$?

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

    Study Notes

    Algebra II Review - Unit 1 & 2

    • Solving Inequalities: Interval notation used to express solutions to inequalities like 2|x + 3| > 6.
    • Absolute Value Equations: Solving equations like |x - 1| - 7 = 2, including finding the sum and product of solutions.
    • Evaluating Functions: Finding the value of a function at a specific input (e.g., f(-3)).
    • Systems of Equations: Finding the product of solutions to a system of two linear equations (e.g., 3x - y + 5 = 0, 2x + 3y - 4 = 0).
    • Lines: Writing equations of lines in slope-intercept form, given points and/or perpendicularity to other lines (e.g., through (-4, 2) perpendicular to y = -x/3 + 2 ).
    • Quadratic Functions: Determining which quadratic equation models a function given multiple points (e.g. (-3, 0), (5, 0), and (1, -32)).
    • Axis of Symmetry: Finding the equation of the axis of symmetry of a parabola through two given points (e.g., (-4, 0), (6, 0)).

    Algebra II Review – Unit 3 & 4

    • Quadratic Functions: Understanding properties like vertex, axis of symmetry, and y-intercept, expressed using different forms (e.g., y = −2(x + 2)(x – 1)).

    • Vertex Form: Understanding how to complete the square to rewrite quadratic functions in the vertex form (e.g., y = −x² − 8x – 7 ).

    • Complex Numbers: Working with complex numbers and performing operations like (3 + i)(7 – 4i). Operations like 3–2i/5+4i

    • Quadratic Functions – Discriminant: Determining the nature of solutions to quadratic equations using the discriminant (e.g., for y = 2x² – 3x +5 , find the discriminant).

    • Intercept Form & Standard Form: Writing quadratic equations in intercept form given a graph, then finding the standard form.

    • Polynomial Functions: Simplifying polynomial expressions and finding factors (e.g., (5x²y + x³y³ – 7xy²) ).

    • **Polynomial Functions - Operations:**Multiplying polynomial expressions (e.g., (2x - 3)(3x + 2)).

    • Solving Polynomial Equations: Application of techniques when given polynomials like 3x² - x - 2).

    • Dividing Polynomials: Performing division and applying the remainder theorem to polynomials (e.g. x –3x² + 2 divided by x + 2 ).

    • Zeros for Polynomials: Finding the zeros of a polynomial with given factors.

    • Equation of Circle: Finding the center and radius of a circle given its equation in general form (e.g., x² − 2x + y² + 6y = −3 ).

    • Graphing Polynomials: Understanding the relationship between graph of a polynomial and its zeros.

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    Description

    This quiz covers key concepts from Algebra II, including solving inequalities, absolute value equations, and evaluating functions. Additionally, it explores systems of equations, writing equations of lines, and understanding quadratic functions. Perfect for reviewing Units 1 and 2 in Algebra II.

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