Linear And Quadratic Equations

Question 1

Zero product property

Answer 1

If two things multiplied together equal zero then at least one of them is zero

Question 2

Difference of squares

Answer 2

x^2-y^2=(x-y)(x+y)

Question 3

What is the factored form of:
(x^2)(y^2)-16?

Answer 3

(xy-4)(xy+4)

Difference of squares ^

Question 4

If x≠y, then (x-y)/(y-x)=?

Answer 4

-1

Question 5

If two equations describe the same line, how many solutions does that system of equations have?
(Like 10x+10y=20, and x+y=2)

Answer 5

Infinitely many

Question 6

what is the Least Common Multiple (LCM) of a set of numbers?

Answer 6

the smallest non-zero whole number that is divisible by all the numbers in the set

Question 7

What is the quadratic expression of this common identity: (x+y)^2

Answer 7

x^2+2xy+y^2

Question 8

What is the quadratic expression of this common identity: (x-y)^2

Answer 8

x^2-2xy+y^2

Question 9

What is the quadratic expression of this common identity: (x-y)(x+y)
*what is this referred to as?

Answer 9

x^2-y^2

Question 10

if a system of two linear equations are not equal to each other, how many solutions does the system have?

Answer 10

1

Question 11

when can you divide by a variable

Answer 11

only when you know that variable is not equal to zero

Question 12

what is the quadratic formula and why would you use it?

Answer 12

formula in pic - use it to find the roots/solutions of a quadratic equation

Question 13

what form does a quadratic equation have to be in to utilize the quadratic formula to solve for its roots

Answer 13

general form: ax^2+bx+c = 0

Question 14

when should you use the quadratic equation vs factoring?

Answer 14

when the expression cannot easily be factored

Question 15

how can you use the discriminant in the quadratic equation to quickly determine the number of roots the equation has (and what is the discriminant)?

Answer 15

discriminant is the portion in the numerator under the radical - the b^2-4ac part. if the discriminant is positive, there are two roots, if it is zero there is one root, if it is negative there are zero roots (no solution). this makes sense since if it was zero, the +/- sqrt(discriminant) would yield the same thing for both +/-

Question 16

what do vieta’s equations say are the sum and products of the solutions to equations (in general form) that have two solutions

Answer 16

sum of the two solutions is -b/a
product is c/a

Question 17

hidden quadratics often contain a variable (x) with no exponent and then the square root of that same variable - what does that look like and how do you get it into quadratic form?

Answer 17

• look at attached picture
  x-8*sqrt(x)+15=0
  step 1: replace x with (sqrt(x))^2
  step 2: replace sqrt(x) with y
  step 3: solve resulting quadratic for y
  step 4: replace y with sqrt(x) and solve for x

Question 18

hidden difference of squares in: squared algebraic expressions

how would you use difference of squares to simplify (2x+1)^2 - (2x-4)^2

Answer 18

(2x+1)^2 - (2x-4)^2 = (2x+1-2x+4)(2x+1+2x-4) = (5)(4x-3) = 20x-15

Question 19

hidden difference of squares in: implied difference of squares

can be helpful in finding the product of two numbers if one of the numbers is k more than some number n and the other is k less than that same number n. ex: 10,004*9,996

Answer 19

10,0049,996 = (10,000+4)(10,000-4) <-difference of squares
= 10,000^2 - 4^2 = 99,999,984

Question 20

hidden difference of squares with roots:

must be familiar with property -> for x>=0, (sqrt(x))^2 = x

Answer 20

look at screenshot pic for work through example