What is a radical expression?
A numerical or algebraic expression written with a square root. Radical expressions need to be simplified.
How do you simplify sqrt(8)?
- Factor it. Make certain that one of your factors is a perfect square: sqrt(4)*sqrt(2)
- Simplify the perfect square radical:
2*sqrt(2)
How do you simplify sqrt(45)?
- Factor it: sqrt(9)*sqrt(5)
2. Simplify: 3*sqrt(5)
How do you simplify sqrt(200)?
- Factor it: sqrt(100)*sqrt(2)
2. Simplify: 10*sqrt(2)
How do I calculate distance between two points on a graph?
Use the pythagorean theorem
Pythagorean Theorem
a^2 + b^2 = c^2
How do you find distance from (-2,5) to (3,1)?
- Draw a right triangle and measure the two legs: For this example, vertical side measures 4 units, while horizontal side measures 5 units.
- Apply pythagorean theorem: 4^2 + 5^2 = c^2.
- Simplify: 16+25 = 41 = c^2.
- Take sqrt. Sqrt(41) = c
Parallel Lines
Parallel lines have SAME SLOPE, but different y-intercepts. They never cross.
Perpendicular Lines
Perpendicular Lines have OPPOSITE RECIPROCAL SLOPES.
If line A has equation y = 3x + 4, what is the slope of a line parallel to it?
m = 3
If line A has equation y = 3x + 4, what is the slope of a line perpendicular to it?
m = -1 / 3
A line is perpendicualar to the line y = -2/5 x + 1 and passes through the point (5,0). How do you find its equation?
- Slope is opposite reciprocal: m = 5/2
- Point is (5,0).
- Insert point and slope into point-slope form: y - k = m(x - h), so y - 0 = 5/2(x - 5).
- Simplify: y = 2.5x - 12.5
Midpoint Formula (Technical)
( (x1 + x2) / 2 , (y1 + y2) / 2 )
Midpoint Formula (concept)
Average of the x and y values!
Always combine…
… like terms
