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SL 1: Chapter 1 (Linear Equations (Standard form: Ax+By=C {A,B&C have…
SL 1: Chapter 1
Linear Equations
Standard form: Ax+By=C {A,B&C have to be whole numbers and A has to be positive
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Parallel: Slope is same, Perpendicular: slopes are opposite
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Midpoint: M=((x+x)/2,(y+y)/2)
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can solve systems with elimination, substitution, matrices, or graphing
Quadratic Equations
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Methods to solve: factor, graph, completing the square, quadratic formula
To complete the square, 1. divide by a term 2. Move constant to other side of =, 3. complete square by adding (b/2)^2 to both sides, 4. then simplify
If discriminant is < 0 = 2 complex solutions: discriminant is 0= 2 equal solutions: discriminant is > 0= 2 real solutions
Losing a root: lose a value of x in calculation, can get it back by setting whatever you cancelled out in the question to 0
Gaining an root: having extraneous solutions, just plug answer back in to see if they match
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Complex Numbers
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Powers of i: i^2= -1, i^3= -i, i^4= 1
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Quadratic Models+Graphs
Line of symmetry: x=-b/2a, use this value in the equation to find the y for vertex coordinate
y-int: when x=0, x-int: when y=0
When graph a quadratic need LOS, vertex, y-int, x-int, at the least
Need three points of the parabola to find it's equation can find by hand, calc, or matrices
height of thrown object model: h(t)=-1/2gt^2+vt+h (g is gravity, h is initial height, and v is initial velocity)