Some Common Algebra Formulas

 

Some Common Algebra Formulas:

1. Quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

This formula is used to solve for the roots of a quadratic equation, which has the form ax^2 + bx + c = 0. The formula gives the two possible values for x that solve the equation.

2. Distance formula:

d = √((x2 - x1)^2 + (y2 - y1)^2)

This formula is used to find the distance between two points in a 2D plane. Given two points (x1, y1) and (x2, y2), the formula gives the straight-line distance between them.

3. Slope-intercept form of a line:

y = mx + b, where m is the slope and b is the y-intercept

This formula gives the equation of a line in the form y = mx + b, where m is the slope and b is the y-intercept. The slope-intercept form is useful because it makes it easy to find the equation of a line given two points on the line, or given the slope and the y-intercept.

4. Point-slope form of a line:

y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line

This formula gives the equation of a line in the form y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. The point-slope form is useful because it makes it easy to find the equation of a line given the slope and a single point on the line.

5. Midpoint formula:

M = (x1 + x2 / 2, y1 + y2 / 2)

This formula is used to find the midpoint of a line segment between two points in a 2D plane. Given two points (x1, y1) and (x2, y2), the formula gives the coordinates of the midpoint.

6. Pythagorean theorem:

a^2 + b^2 = c^2, where c is the hypotenuse and a and b are the legs

This theorem states that in a right triangle, the sum of the squares of the lengths of the two smaller sides is equal to the square of the length of the largest side, called the hypotenuse.

7. Factoring a quadratic:

a(x - h)^2 + k, where (h, k) is the vertex

A quadratic can be factored into the form a(x - h)^2 + k, where (h, k) is the vertex of the parabola. Factoring a quadratic can be useful for solving for the roots of the equation or for graphically understanding the shape of the parabola.

8. Standard form of a parabola:

y = ax^2 + bx + c

This form of a parabola is written as y = ax^2 + bx + c, where a, b, and c are constants. The standard form makes it easy to graph a parabola and to see the properties of the parabola, such as the vertex, axis of symmetry, and the x and y intercepts.

9. Simplifying expressions:

a(b + c) = ab + ac, (a + b)^2 = a^2 + 2ab + b^2

Simplifying expressions is the process of making an expression easier to understand or easier to work with. For example, the first example given is the distributive property, which states that multiplying a sum by a factor is the same as multiplying each term of the sum by the factor. The second example given is the expansion of a square, which gives the formula for finding the square of a binomial.

10. Solving linear equations:

a(x) + b = c, x = (c - b) / a.

Solving linear equations is the process of finding the value of the variable that makes the equation true. In the given formula, x = (c - b) / a, a, b, and c are constants, and x is the variable being solved for.