Algebra 3.4-3.7

f(x)= a|x| -when a is a fraction, what is the graph called? -when a is a positive whole number what is it called? see notes

-fraction= vertical shrink (more wide) -positive whole number= vertical stretch (more narrow)

y= a|x+h| + k -whats the vertex? -slope ish? -if a>0, which way does the V graph go? -if a<0, which way does the V graph go?

-vertex= (-h, k) -kinda slope= a - it goes up -it goes down see notes

for cramer's law, if you get 0/0 whats the answer? What about 5/0?

0/0= inf solutions. same line 5/0= no solution bcuz parallel lines.

What are the four ways to solve systems of equations?

1= graphs 2= substitution 3= linear combination 4= cramer's rule

Graphing systems of inequalities: y≤ # do what? y ≥ # x ≤ # x ≥ # x or y < or > # x or y ≤ or ≥ #

1= shade below 2= shade above 3= shade left 4= shade right 5= dotted line 6= non dotted line

What are the 3 types of ways to use as the equations of lines? -when do u use them

1= slope intercept form y=mx+b -use when given y intercept 2=Point slope form y-y1=m(x-x1) -if not given y intercept use. use this one most of the time 3= standard form Ax+By= C -ALWAYS end your equation in standard form -A can not be negative -A,B,and C aren't fractions

What do these mean? 1) y= |x-2| 2) y= |x+7|

1=graph goes two to the right -if negative, go right 2= graph goes 7 to the left -if positive go left

Graph the system of inequalities: x+2y ≤ 6 x-3y ≥ 6 x+2 > 0 what do you do?

WHENEVER IT ASKS YOU TO "GRAPH", YOU GRAPH THE EQUATIONS AND THEN FIND THE AREAS WHERE THEY OVERLAP -first put them in slope intercept form to graph them

What does this mean? y= -3|x+2|+ 1

slope= -3 2 to the left up 1 vertex= (-2, 1)

when solving systems of equations, what if you get a number (instead of something normal like x=1), -10=1? What does this mean? What if you got an answer like 19=19

the answer is no solution. parallel -inf. solutions. they're on the same line.

Whenever you have problems like "Find the equation of a line through (x,y) with NO SLOPE or ZERO SLOPE" What do u do?

graph it!

When the problem says "solve the system of eqautions by graph:" y-x=3 y+2x= -3 What do you do?

graph the two equations and find the point where they intersect

Practice problem: (tricky one) Find the equation of a line through (6, 1) with no slope

just graph it! see notes answer: x=6

Practice problem: Find the equation of the line. You have a line with points (-1, 5) and (3, 6)

m= (5-6) ---------- (-1-3) m= 1/4 y-6=1/4(x--3) 4y-24=x-3 Now put in standard form= x-4y= -21