Heart of algebra Flashcards
Linear equations
There are three sets of necessary criteria an equation has to meet in order to qualify as a linear one: an equation expressing a linear relationship can’t consist of more than two variables, all of the variables in an equation must be to the first power, and the equation must graph as a straight line.
Interperting functions (ex. 2500+3.50t) what does t mean?
Practise on khan academy
Typer of models to interpet (Linear, quadratic and exponential) their equations
Linear: standard: y=mx+b. Ax+by=c. y-y1=m(x-x1)
Quadratic: y = ax squared +bx+c, y=a(x-p)(x-q), y=a(x-h) squared +k
Exponetion: y=ab squared x
What is linear, quadratic and exponential used for
Linear used for slope, y-intercept and x intercept
Quadratic used for vertex, y-intercept and x intercept/ zero
Exponentional used for initial value, final value, rate of change
Calcuste slope between two points ehst formula would you use?
(use formal, m=y2-y1/ x2-x1)
Slope x=3 y=4 how would you write it.
Slope = 4/3 (rise/run)
How to solve B, when given x and y. Mx+b
Mx+b. So you plug in x and y and solve to find b
Grapghing linear inequalities
Ex. y<3x+1
Slope = 3/1. y -intercept = 1. We graph it the same but wherenevre we have a equality we need to shade the graph, if y function we graph above.
Abolsute value. Ex. -[x-3]. graph
We know -3=3 and since there is a negative it sill go down. If number is outside ex. [x]+1. We go up one y axis, then graph above. So when inside bracket it affects x-axis. When outside bracket it affects x=y axis
Constant =
value that does not change
Solving linear equations when given m,b. Ex. m = 2, b = -3/ With this equation write the equation in slope intercept form and point form
Slope intercept = y=2x-3. Point form = y+3=2x(x-0)
When given m,p (x,y)
Ex. m=2. P(1,3)
y=2x+3
y2-y1=m(x2-x1)
Point slope = y2-3=m(x2-1)
When given two points, what formula to use?
When given two points. Use m=y2-y1/ x2-x1
Expoennts mulitplacation. If bases are the same,
Then you add the exponent
Quadratic rwuations. A squared - b squared =
(a+b) (a-b)
Solving quadratic equations with only 2 numbers. Ex 16x squared -64=0.
To solve this we do 16(x2-4). 16(x+2) (x-2).
rpaghing quadratic equatuibs. Ex (x+1) squared
x-axis =-1. and it goes up
Axis of symmetry is
the middle line
Vertex form. and how to grpagh
=a(x-h) squared +k. V(h,k). To graph vertex form. Do a table. And plug in x for numbers to find x=-b/2a. Then plug in to find y verex
To find vertex in standard form,
Use -b/2a to solve for x then plug in to find y .
Grapghing standard form.
1 step. Check to see if tis factorbale, to find x. (2) to find x-intercept replace y with 0. Then just plug in x into equation to find the y-value also they must be the corresponding.
Complete the square
y=x2-4x+2
y=x2-4x+2 y=x2-4x+2 squared- 2 squared + 2 y=(x-2) squared -4 +2 y=(x-2) squared -2 Vertex = (2, -2) Complete the square means taking B and squaring it. So square root 4=2 squared. Now we add it to the other side or subtract 2 square don the same side. Now we can factor, by first putting x and the sign after it, then putting c
Domain and range
The domain and range are defined for a relation and they are the sets of all the x-coordinates and all the y-coordinates of ordered pairs respectively. For example, if the relation is, R = {(1, 2), (2, 2), (3, 3), (4, 3)}, then:
Domain = the set of all x-coordinates = {1, 2, 3, 4}
Range = the set of all y-coordinates = {2, 3}
Logs
= logb n. For example, 23 = 8; therefore, 3 is the logarithm of 8 to base 2, or 3 = log2 8.
