10 Questions
What is the method used to solve linear systems by replacing one equation with the expression from another equation?
Substitution
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)?
((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 ___.
y-intercept
What is the method used to solve quadratic equations when factoring is not possible?
Quadratic Formula
A quadratic relation in vertex form is y = a(x - h)^2 + k.
True
What is the axis of symmetry of a parabola in vertex form y = a(x - h)^2 + k?
x = h
Match the forms of quadratic relations with their characteristics:
Standard Form = y = ax^2 + bx + c Vertex Form = y = a(x - h)^2 + k Factored Form = y = a(x - r)(x - s)
The quadratic formula is x = (-b ± √___)/2a, where ___ is the discriminant.
b^2 - 4ac
What is the method used to convert a quadratic relation from standard form to vertex form?
Completing the Square
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
Test your understanding of linear systems, analytic geometry, and graphing. Covers calculating line lengths, midpoints, solving linear systems, and graph analysis.
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