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Section 1

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How to multiply groups

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Algebra Math

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Mar 14, 2020

Cards (33)

Section 1

(33 cards)

How to multiply groups

Front

FOIL: Front Inside Outside Last Ex: (2x + 4)(3x - 7) 6x^2 - 14x + 12x -28 6x^2 -2x -28

Back

Multiplication with exponents

Front

Example: (x^5)(x^3) = x^8

Back

Quadratic Form

Front

Back

Practice: Solve x^2 - 5x - 6 = 0

Front

Remember to factor first! (x - 6)(x + 1) = 0 Set each term equal to 0 and solve for x: x - 6 = 0 x + 1 = 0 Solution: x = 6, -1

Back

Associative property of addition

Front

Example: g + (11h + 9h) = (g + 11h) + 9h

Back

multiplicative inverse

Front

A number times its multiplicative inverse is equal to 1; also called reciprocal

Back

Simplify (a + b)(a + b)

Front

(a + b)^2

Back

zero property of multiplication

Front

Example:

Back

How to check your factoring on a graphing calculator

Front

1. Go to Y = 2. Enter the original formula under Y1 3. Enter your solution as Y2 4. Go to graph or table: are they the same? If so, congratulations, you did it! If not, go through and check your signs :)

Back

distributive property

Front

multiplying a number by a group of numbers added together is the same as doing each multiplication separately

Back

Coefficient

Front

The numerical factor of a term. The number before the variable.

Back

reciprocal

Front

one of two numbers whose product is 1; also called multiplicative inverse

Back

Difference of Squares

Front

Back

Associative property of multiplication

Front

Example: (3c) x 5 = 3(c x 5)

Back

Kick this test's butt!

Front

You can do it!

Back

Identity property of addition

Front

Example:

Back

How to solve an equation

Front

1. Make sure all terms are on the same side, and the other side equals zero 2. Pull (factor) out any like (common) terms (using distributive property) 3. In quadratic form, is there an a and a negative c value, but no b? If so, are a and c squares? If so, apply the difference of squares. 4. Otherwise, factor the equation using the X method 5. Once every term is multiplied by every other term, set each term equal to zero (anything inside of parenthesis counts as a term, so 2x(x + 4)(x-7) fits this bill). In this example, solve 2x = 0, x + 4 = 0, x - 7 = 0. Solutions are x = 0, -4, 7

Back

Commutative property of multiplication

Front

Example: (ab)c = (ba)c

Back

Practice: Solve x^2 - 5x + 6 = 0

Front

Remember to factor first! (x - 2)(x - 3) = 0 Set each term equal to 0 and solve for x: x - 2 = 0 x - 3 = 0 Solution: x = 2, 3

Back

Commutative property of addition

Front

Example: 2 + 5 = 5 + 2

Back

Factoring out like (common) terms

Front

Can every term in the equation be divided by something? If so, you can factor it out. Examples: 1: 7x^2 + 2x = x (7x + 2) 2: 14x^2 + 6x + 8 = 2 (7x^2 + 3x + 4) 3: 6n^3 + 18n^2 + 3n = 3n (2n^2 + 6n + 1)

Back

Identity property of multiplication

Front

Example:

Back

Division with exponents

Front

Example: x^5 / x^3 = x^2

Back

Axis of Symmetry

Front

A vertical line that divides the parabola into two congruent halves

Back

Does the parabola point up or down?

Front

What is the 'a' term (in front of the x^2)? If it's positive, the curve goes up & the vertex is the lowest point. If it's negative, the curve goes down & the vertex is the highest point

Back

Practice: Solve 9x^2 - 25 = 0

Front

Remember difference of squares! (3x - 5)(3x + 5) = 0 Set each term equal to 0 and solve for x: 3x - 5 = 0 3x + 5 = 0 Solution: -5/3, 5/3

Back

Practice: Solve -6x^2 - x + 2 = 0

Front

Remember to factor first! (-2x + 1)(3x + 2) Set each term equal to 0 and solve for x: -2x + 1 = 0 3x + 2 = 0 Solution: 1/2, -2/3

Back

Term

Front

A single number or the product of a number and one or more variables.

Back

Practice: Solve x^2 + 5x + 6 = 0

Front

Remember to factor first! (x + 2)(x + 3) = 0 Set each term equal to 0 and solve for x: x + 2 = 0 x + 3 = 0 Solution: x = -2, -3

Back

multiplication property of -1

Front

Example: y(-1) = -y -(d + 3) = -1(d + 3)

Back

Vertex of Parabola

Front

The point where the parabola crosses its axis of symmetry. The x-coordinate is the axis of symmetry, -b/(2a) For the y-coordinate: you can plug your x-value into your original equation to get the y-value for that point. You can also use this equation: (4ac - b^2) / (2a) (don't forget the parenthesis), but don't worry about memorizing it right now

Back

How to graph an equation

Front

1. Find the axis of symmetry (x = -b/(2a)) 2. Find the vertex (x = -b/(2a), to get y, plug the x value into the original equation 3. Find the y-intercept (in quadratic form, y-intercept is (0, c) 4. Find additional points on the graph by plugging x-values into your original equation Hint 1: The points will be mirrored through the axis of symmetry, so if x = 1 is the axis of symmetry, and the y-intercept is (0, 5), there's also a point at (2, 5) Hint 2: If you set y equal to 0 and solve the equation through factoring, you'll find the x-intercepts (ex: (x - 3)(x+4) = 0, there's two points (3, 0) and (-4, 0)

Back

Practice: Solve x^2 - 16 = 0

Front

Remember difference of squares! (x - 4)(x + 4) Set each term equal to 0 and solve for x: x - 4 = 0 x + 4 = 0 Solution: x = -4, 4

Back