Advanced Algebra Unit 6 Review

Questions and Answers

Which of the following is the slope-intercept form of a linear equation?

(y - y1) = m(x - x1)

Ax + By = C

y = mx + b (correct)

x = a

What shape does an absolute value function create on a graph?

V-shaped

A quadratic function creates a U-shaped graph.

True

What is the standard form of a quadratic equation?

y = ax^2 + bx + c Signup and view all the answers

What is the vertex form of a quadratic equation?

y = a(x - h)^2 + k Signup and view all the answers

What describes the shape of an exponential function's graph?

J-shaped curve Signup and view all the answers

The formula to find the slope of a line is the change in over the change in .

y, x Signup and view all the answers

For the equation y = mx + b, what does 'm' represent?

slope Signup and view all the answers

What is the formula for the area of a rectangle?

Area = Length x Width Signup and view all the answers

What is the formula for the perimeter of a rectangle?

Perimeter = 2(Length + Width) Signup and view all the answers

What is the first step in performing polynomial operations?

Put the polynomial in standard form. Signup and view all the answers

What do you need to factor out from a polynomial expression?

greatest common factor (GCF) Signup and view all the answers

Match the following polynomial expressions with their classifications:

5x^2 - 3x + 2 = Quadratic 5x + 2 = Linear 3x^3 + 2x^2 + 3x + 4 = Cubic 8x^4 = Quartic 5x^5 + 3x = Quintic 8x^8 + 6x^2 + 7x - 2 = Degree 8 Signup and view all the answers

Study Notes

Linear Functions

Linear functions have a constant rate of change, yielding straight-line graphs.
Key equations:
- Slope-intercept form: (y = mx + b) (m = slope, b = y-intercept)
- Point-slope form: ((y - y_1) = m(x - x_1))
- Standard form: (Ax + By = C)
- Vertical line: (x = a)
- Horizontal line: (y = b)
Slope calculation: (\text{slope} = \frac{\Delta y}{\Delta x})

Absolute Value Functions

Absolute value functions yield V-shaped graphs and measure distance from zero.
Vertex form: (y = a|x - h| + k) (h, k is the vertex)

Quadratic Functions

Quadratic functions create U-shaped graphs, known as parabolas.
Standard form: (y = ax^2 + bx + c)
Factored form: (y = a(x - r_1)(x - r_2)) where (r_1) and (r_2) are roots.
Vertex form: (y = a(x - h)^2 + k) (h, k is the vertex)

Exponential Functions

Exponential functions display a J-shaped curve on graphs.
General equation: (y = a(b)^{x - h} + k) (b = constant ratio, h represents horizontal shift, k represents vertical shift)

Piecewise Functions

Evaluate values of piecewise functions by examining defined intervals.
Key elements include determining domain (all possible x-values) and range (all possible y-values).

Polynomials

Area of a rectangle: ( \text{Area} = \text{Length} \times \text{Width} )
Perimeter is the summation of all sides.
Operations on polynomials must result in expressions in standard form.

Polynomial Operations

To simplify expressions, ensure polynomials are in standard form after performing operations.
Factoring out the greatest common factor is critical for simplifying polynomial expressions.

Classification of Polynomials

Monomial: a single term (e.g., (5x^5))
Binomial: two terms (e.g., (3x + 2))
Trinomial: three terms (e.g., (x^2 + 3x + 4))
Highest degree indicates polynomial classification (e.g., cubic, quadratic, linear).

Description

Prepare for your Unit 6 Final Exam in Advanced Algebra focusing on function families, specifically linear functions. This quiz covers important concepts such as slope-intercept form and identifying properties of linear equations. Test your knowledge and ensure you're ready to ace the exam!