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Questions and Answers
Which of the following is the slope-intercept form of a linear equation?
Which of the following is the slope-intercept form of a linear equation?
What shape does an absolute value function create on a graph?
What shape does an absolute value function create on a graph?
V-shaped
A quadratic function creates a U-shaped graph.
A quadratic function creates a U-shaped graph.
True
What is the standard form of a quadratic equation?
What is the standard form of a quadratic equation?
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What is the vertex form of a quadratic equation?
What is the vertex form of a quadratic equation?
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What describes the shape of an exponential function's graph?
What describes the shape of an exponential function's graph?
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The formula to find the slope of a line is the change in ______ over the change in ______.
The formula to find the slope of a line is the change in ______ over the change in ______.
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For the equation y = mx + b, what does 'm' represent?
For the equation y = mx + b, what does 'm' represent?
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What is the formula for the area of a rectangle?
What is the formula for the area of a rectangle?
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What is the formula for the perimeter of a rectangle?
What is the formula for the perimeter of a rectangle?
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What is the first step in performing polynomial operations?
What is the first step in performing polynomial operations?
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What do you need to factor out from a polynomial expression?
What do you need to factor out from a polynomial expression?
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Match the following polynomial expressions with their classifications:
Match the following polynomial expressions with their classifications:
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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).
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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!
