Podcast
Questions and Answers
What is the method used to solve linear systems by replacing one equation with the expression from another equation?
What is the method used to solve linear systems by replacing one equation with the expression from another equation?
A linear system with two parallel lines has one solution.
A linear system with two parallel lines has one solution.
False
What is the formula to find the midpoint of a line segment with endpoints (x1, y1) and (x2, y2)?
What is the formula to find the midpoint of a line segment with endpoints (x1, y1) and (x2, y2)?
((x1 + x2)/2, (y1 + y2)/2)
The equation of a line in slope-intercept form is y = mx + ___, where m is the slope and b is the ___.
The equation of a line in slope-intercept form is y = mx + ___, where m is the slope and b is the ___.
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What is the method used to solve quadratic equations when factoring is not possible?
What is the method used to solve quadratic equations when factoring is not possible?
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A quadratic relation in vertex form is y = a(x - h)^2 + k.
A quadratic relation in vertex form is y = a(x - h)^2 + k.
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What is the axis of symmetry of a parabola in vertex form y = a(x - h)^2 + k?
What is the axis of symmetry of a parabola in vertex form y = a(x - h)^2 + k?
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Match the forms of quadratic relations with their characteristics:
Match the forms of quadratic relations with their characteristics:
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The quadratic formula is x = (-b ± √___)/2a, where ___ is the discriminant.
The quadratic formula is x = (-b ± √___)/2a, where ___ is the discriminant.
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What is the method used to convert a quadratic relation from standard form to vertex form?
What is the method used to convert a quadratic relation from standard form to vertex form?
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Study Notes
Linear Systems & Analytic Geometry
- Calculate the length of a line and midpoints
- Solve linear systems using graphing, substitution, or elimination and check solutions
- Identify the number of solutions to a linear system based on its graph: zero, one, or infinite solutions
- Use line lengths and slopes to prove geometric shapes, such as right triangles, parallelograms, rectangles, etc.
- Determine the equation of a line (median, right/perpendicular bisector, altitude of a triangle)
- Calculate the shortest distance from a point to a line (length of an altitude)
Quadratic Relations and Equations
- Factor quadratic expressions: ax2 + bx + c for all factor types (a = 1, a ≠ 1, difference of squares, perfect squares, factor by grouping)
- Solve quadratic equations by factoring and state solutions
- Solve quadratic equations using the quadratic formula
- Determine the number of solutions to a quadratic equation and whether it is factorable
- Identify key characteristics of a graph: y-intercept, x-intercepts, vertex, equation of axis of symmetry, max/min value
- Convert between standard, vertex, and factored forms of quadratic relations
- Graph a parabola by finding vertex, x-intercepts, y-intercept, and other points
- Solve max and min problems using an equation and determining the vertex by completing the square or averaging intercepts
Trigonometry
- Understand similar triangles
- Apply SOH CAH TOA to right angle triangles
- Use the Sine Law and Cosine Law to solve triangular problems
- Apply trigonometry to real-world applications: angle of elevation and angle of depression
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Description
Test your understanding of linear systems, analytic geometry, and graphing. Covers calculating line lengths, midpoints, solving linear systems, and graph analysis.
