math final

absolute value

100

how do you know if the graph is a function?

if it passes the vertical line test( a straight line that touches the graph once).

200

what shape does an absolute make when graphing?

A v shape

300

If the equation is lx-70l where does that move the graph to?

70 units to the right

400

solve -4=1/2 /x-3/-2

there's no solution because you an absolute value can be an answer when it's a negative

500

solve algebraically lx-3l>1

x>4,x<2

trinominal

100

what is the first step solving a trinomial

A times b and finding variables that add to B and multiply to A times C

200

2x^2+13x-7

AxC= -14 B=2 

What is the next step 

2x^2-X+14-7

300

3x^2+16x+21=0

^{what is the answer}

3x^{2+7x+9x+21           axc=63 b=7}

^{x(3x+7)+3(3x+7)}

^{3x+7=0                    x+3=0}

 ^{x=-7/3                           x=-3}

400

how do you solve 10x²-x-21

  find factors that is equal to AxC and that goes into b

10x²-15x+14x-21

what's one factor that you can take out(5)

5x(2x-3) +7(2x-3)

2x-3=0             5x+7=0

x=3/2                   x=-7/5

500

solve x^2+9x+18

what factors go into axc and b (3,68)

x^2+3x+68x+18

factor out x 

x(x+3) +6(x+3) 

x+3=0    x+6=0

x=-3         x=-6

binomial

100

multiply the binomial  (3x+4)(3x-4)

The difference of two squares 

take the square root of the first term (3x)

take the square root out of the second term (4)

9x²-16

200

multiply the binomial (5x-9)(5x+9)

the difference of two squares 

take the square root of the first term(5x)

take the second term out of the second term(9)

25x²-81

300

multiply the binomial (x-4)(x+4)

the difference between two squares

take the first term out of the first term(x²)

take the term out of the second term(4)

x²-16

400

multiply the binomial (2x+5)(2x-5)

the difference of two squares  

take the square root of the first term =2x

take the square root of the second term=5

take the first (add the second term) (the first term-5)

(2x+5)(2x-5)

4x²-25

500

multiply the binomial (2x+4) (2x+4)

the difference between two squares 

Take the square root out of the first term(2x)

take the square root out of the second term(4)

2x²+16

parabola

100

what shape does a parabola make

a U shape

200

what is the formula when solving a parabola

y=x²

300

solve x²-12=0

square roof of x² = square root of 12

after we do that we factor out x²

find factors

x²=+or- 2 square root 3

x²=+or-2 square root 3

400

which best describes this equation when graphing?

y=2(4+2)+1

a-v shape

b- U shape

c- S shape

The answer is b and this is because it's parabola which is a U shape

500

after your done graphing a parabola should you have the y intercept in ordered pairs?

yes and this is because every y intercept needs order pairs when there're points on a graph.

polynomial

100

how do you find the Dagree for a polynomial

the biggest exponent 

200

how do you find the y-intercept from a polynomial function in ordered pairs?

It's the last number in the equation 

example problem-Y=x³+7x-3 

the y-intercept would be (-3,0) in ordered pairs

300

how do you find the # of turning points in a polynomial function

once you find the degree which is the highest exponent you subtract that from one which will be your answer

f(x)=8x²+3x-4

2-1=1 There is 1 turning point possible in the graph

400

what's the formula equation for a polynomial

y=x³

500

when graphing a polynomial will you ever find the range or domain in ordered pairs?

no and this is because when graphing you will always go up,down and going to the sides