Algebra & Geometry Chapter 8-9 Quiz

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Questions and Answers

Use the distributive property to expand the expression $(2x+3)(x-5)$.

$2x^2 - 7x - 15$

Factor the quadratic trinomial $x^2 + 5x + 6$.

$(x + 3)(x + 2)$

Prove that the diagonals of a rectangle are congruent.

Let $ABCD$ be a rectangle. Draw diagonal $AC$. Then, $ riangle ABC$ is a right triangle with $AC$ as its hypotenuse. Similarly, $ riangle ADC$ is a right triangle with $AC$ as its hypotenuse. By the Pythagorean theorem, $AC^2 = AB^2 + BC^2 = AD^2 + DC^2$. Therefore, $AB^2 + BC^2 = AD^2 + DC^2$, so $AB = AD$ and $BC = DC$. Thus, the diagonals of a rectangle are congruent.

Solve the quadratic equation $x^2 + 4x + 4 = 0$ by factoring.

<p>Let $x^2 + 4x + 4 = 0$. Then, $(x + 2)(x + 2) = 0$. Therefore, $x + 2 = 0$, so $x = -2$. Thus, the solution is $x = -2$.</p> Signup and view all the answers

Use the Pythagorean theorem to find the length of the hypotenuse of a right triangle with legs of length 5 and 12.

<p>Let $c$ be the length of the hypotenuse. Then, $c^2 = 5^2 + 12^2$. Therefore, $c = \/sqrt{5^2 + 12^2} = \/sqrt{25 + 144} = \/sqrt{169} = 13$. Thus, the length of the hypotenuse is 13.</p> Signup and view all the answers

If $f(x) = (x - 2)(x + 3)$, what is the value of $f(-1)$?

<p>-8</p> Signup and view all the answers

What is the axis of symmetry of the graph of the quadratic function $y = x^2 + 2x + 1$?

<p>The axis of symmetry is $x = -1$.</p> Signup and view all the answers

If $p(x) = x^2 - 4x - 3$ and $q(x) = x^2 - 7x + 12$, what is the value of $p(-2) + q(3)$?

<p>7</p> Signup and view all the answers

What is the factored form of the quadratic expression $x^2 - 5x - 6$?

<p>$(x - 6)(x + 1)$</p> Signup and view all the answers

If $f(x) = x^2 + 2x + 1$ and $g(x) = x - 1$, what is the value of $f(g(2))$?

<p>6</p> Signup and view all the answers

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Study Notes

Algebra

  • Chapter 8 covers polynomials, including:
    • Using the distributive property (Lesson 8.5)
    • Factoring quadratic trinomials (Lesson 8.6)
    • Factoring special products (Lesson 8.7)

Algebra

  • Chapter 9 focuses on quadratic functions and equations, including:
    • Graphing quadratic functions (Lesson 9.1)
    • Solving quadratic equations by factoring (Lesson 9.4)

Geometry

  • Chapter 6 explores quadrilaterals, including:
    • Angles of polygons (Lesson 6.1)
    • Parallelograms (Lesson 6.2)
    • Tests for parallelograms (Lesson 6.3)
    • Special parallelograms: Rectangles (Lesson 6.4)

Geometry

  • Chapter 8 covers right triangles and trigonometry, including:
    • The Pythagorean theorem and its converse (Lesson 8.2)
    • Special right triangles (Lesson 8.3)
    • Trigonometry (Lesson 8.4)

Algebra Chapters

  • The two chapters covered in Algebra are Chapter 8: Polynomials and Chapter 9: Quadratic functions and equations.

Chapter 8: Polynomials

  • Chapter 8 consists of three lessons: 8.5, 8.6, and 8.7.
  • Lesson 8.5 focuses on using the distributive property.
  • Lesson 8.6 covers factoring quadratic trinomials.
  • Lesson 8.7 is about factoring special products.

Chapter 9: Quadratic functions and equations

  • Chapter 9 consists of at least two lessons: 9.1 and 9.4.
  • Lesson 9.1 teaches graphing quadratic functions.
  • Lesson 9.4 covers solving quadratic equations by factoring.

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