Podcast
Questions and Answers
What is the quadratic formula?
What is the quadratic formula?
- x=-b±[√b²-4ac]/2(a) (correct)
- -b±[√b²-4ac] (correct)
- x=-b/[2(a)]
- 2a+b
What is the point-slope form of a line?
What is the point-slope form of a line?
y - y1 = m(x - x1)
What is the standard form of a linear equation?
What is the standard form of a linear equation?
Ax + By = C
What does 'c*' represent?
What does 'c*' represent?
What is the slope equation?
What is the slope equation?
What is the slope-intercept form of a line?
What is the slope-intercept form of a line?
What is the discriminant formula?
What is the discriminant formula?
What does a greater than (>) graph point resemble?
What does a greater than (>) graph point resemble?
What does a less than (<) graph point resemble?
What does a less than (<) graph point resemble?
What is the representation of an absolute value graph?
What is the representation of an absolute value graph?
How is the 'greater than or equal to' notation represented?
How is the 'greater than or equal to' notation represented?
How is the 'less than or equal to' notation represented?
How is the 'less than or equal to' notation represented?
What is set notation represented as?
What is set notation represented as?
What does interval notation (-∞, ∞) indicate?
What does interval notation (-∞, ∞) indicate?
If the slope (m) is greater than 0, how is the line oriented?
If the slope (m) is greater than 0, how is the line oriented?
If the slope (m) is less than 0, how is the line shaded?
If the slope (m) is less than 0, how is the line shaded?
What does the equation y = a|x - h| + k represent?
What does the equation y = a|x - h| + k represent?
What does x/0 represent?
What does x/0 represent?
What does 0/x represent?
What does 0/x represent?
What does the symbol / indicate in relation to absolute value?
What does the symbol / indicate in relation to absolute value?
What does the symbol /\ indicate in relation to absolute value?
What does the symbol /\ indicate in relation to absolute value?
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Study Notes
Quadratic Functions
- Quadratic formula:
( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ) - Discriminant:
( b^2 - 4ac ); determines the nature of the roots of a quadratic equation.
Linear Functions
- Point-slope form:
( y - y_1 = m(x - x_1) ); used to write the equation of a line given a point and slope. - Standard form:
( Ax + By = C ); where A, B, and C are integers, often used for easier identification of intercepts. - Slope-intercept form:
( y = mx + b ); where m is the slope and b is the y-intercept of the line. - Slope equation:
( \frac{y_2 - y_1}{x_2 - x_1} ); calculates the slope between two points.
Graphing Inequalities
- Graphing ( y > k ): Curve opens upwards indicating the region above a line.
- Graphing ( y < k ): Curve opens downwards indicating the region below a line.
- Greater than or equal to (≥): Includes solid line and shaded above.
- Less than or equal to (≤): Includes solid line and shaded below.
Absolute Value Functions
- Absolute value graph represented as V-shape (|/); the vertex indicates the minimum or maximum point of the graph.
- Equation format ( y = a|x - h| + k ); vertex occurs at point (h, k).
Set and Interval Notation
- Set notation example: ( { x | x > b } ); describes a set of values x greater than b.
- Interval notation: ( (-\infty, \infty) ); represents all real numbers, often used to express the domain or range.
Undefined and Horizontal Lines
- Division by zero results in undefined; indicates a vertical line.
- Any number divided by zero results in a horizontal line at y = 0.
Additional Notes
- If slope (m) is >0: line is inclined upwards (/).
- If slope (m) is <0: line is inclined downwards ().
- For conditions involving absolute value:
- Downward-pointing curve represents negative slopes.
- Upward-pointing curve represents positive slopes.
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