Heart of algebra

Question 1

Linear equations

Answer 1

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.

Question 2

Interperting functions (ex. 2500+3.50t) what does t mean?

Answer 2

Practise on khan academy

Question 3

Typer of models to interpet (Linear, quadratic and exponential) their equations

Answer 3

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

Question 4

What is linear, quadratic and exponential used for

Answer 4

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

Question 5

Calcuste slope between two points ehst formula would you use?

Answer 5

(use formal, m=y2-y1/ x2-x1)

Question 6

Slope x=3 y=4 how would you write it.

Answer 6

Slope = 4/3 (rise/run)

Question 7

How to solve B, when given x and y. Mx+b

Answer 7

Mx+b. So you plug in x and y and solve to find b

Question 8

Grapghing linear inequalities

Ex. y<3x+1

Answer 8

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.

Question 9

Abolsute value. Ex. -[x-3]. graph

Answer 9

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

Question 10

Constant =

Answer 10

value that does not change

Question 11

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

Answer 11

Slope intercept = y=2x-3. Point form = y+3=2x(x-0)

Question 12

When given m,p (x,y)

Ex. m=2. P(1,3)

Answer 12

y=2x+3
y2-y1=m(x2-x1)
Point slope = y2-3=m(x2-1)

Question 13

When given two points, what formula to use?

Answer 13

When given two points. Use m=y2-y1/ x2-x1

Question 14

Expoennts mulitplacation. If bases are the same,

Answer 14

Then you add the exponent

Question 15

Quadratic rwuations. A squared - b squared =

Answer 15

(a+b) (a-b)

Question 16

Solving quadratic equations with only 2 numbers. Ex 16x squared -64=0.

Answer 16

To solve this we do 16(x2-4). 16(x+2) (x-2).

Question 17

rpaghing quadratic equatuibs. Ex (x+1) squared

Answer 17

x-axis =-1. and it goes up

Question 18

Axis of symmetry is

Answer 18

the middle line

Question 19

Vertex form. and how to grpagh

Answer 19

=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

Question 20

To find vertex in standard form,

Answer 20

Use -b/2a to solve for x then plug in to find y .

Question 21

Grapghing standard form.

Answer 21

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.

Question 22

Complete the square

y=x2-4x+2

Answer 22

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

Question 23

Domain and range

Answer 23

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}

Question 24

Logs

Answer 24

= logb n. For example, 23 = 8; therefore, 3 is the logarithm of 8 to base 2, or 3 = log2 8.