10 Questions
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.
Let $x^2 + 4x + 4 = 0$. Then, $(x + 2)(x + 2) = 0$. Therefore, $x + 2 = 0$, so $x = -2$. Thus, the solution is $x = -2$.
Use the Pythagorean theorem to find the length of the hypotenuse of a right triangle with legs of length 5 and 12.
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.
If $f(x) = (x - 2)(x + 3)$, what is the value of $f(-1)$?
-8
What is the axis of symmetry of the graph of the quadratic function $y = x^2 + 2x + 1$?
The axis of symmetry is $x = -1$.
If $p(x) = x^2 - 4x - 3$ and $q(x) = x^2 - 7x + 12$, what is the value of $p(-2) + q(3)$?
7
What is the factored form of the quadratic expression $x^2 - 5x - 6$?
$(x - 6)(x + 1)$
If $f(x) = x^2 + 2x + 1$ and $g(x) = x - 1$, what is the value of $f(g(2))$?
6
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.
Test your knowledge on chapters 8 and 9 of Algebra, covering topics such as polynomials, quadratic functions, and equations, as well as Geometry chapter 6 on quadrilaterals.
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