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Algebra 1 Formulas

Algebra 1 Cumulative

A cumulative formula sheet for students taking Algebra 1.

Linear Equations and Inequalities

Slope Formula

m=y2−y1x2−x1m=\frac{y_2-y_1}{x_2-x_1}

Linear Equations and Inequalities

Slope-Intercept Form

y=mx+by=mx+b

The variable "m" is the slope, and "b" is the y-intercept.

Example

In the equation y=2x+5, the slope is 2, and the y-intercept is 5.

Linear Equations and Inequalities

Point-Slope Form

y−y1=m(x−x1)y-y_1=m(x-x_1)

A way of writing a linear equation using the slope and one point the line passes through.

Linear Equations and Inequalities

Standard Form in Linear Equations

Ax+By=CAx+By=C

Exponents and Radicals

Product Rule

xa⋅xb=xa+bx^a\cdot x^b=x^{a+b}

Exponents and Radicals

Quotient Rule

xaxb=xa−b\frac{x^a}{x^b}=x^{a-b}

Exponents and Radicals

Power Rule

(xa)b=xab(x^a)^b=x^{ab}

Exponents and Radicals

Negative Exponent Rule

x−a=1xax^{-a}=\frac{1}{x^a}

Exponents and Radicals

Zero Exponent Rule

x0=1x^0=1

Exponents and Radicals

Product Property (Radicals)

ab=a⋅b\sqrt{ab}=\sqrt{a}\cdot \sqrt{b}

Exponents and Radicals

Quotient Property (Radicals)

ab=ab\sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}

Exponents and Radicals

Fractional Exponent

xmn=xmnx^{\frac{m}{n}}=\sqrt[n]{x^m}

Sequences

Arithmetic Sequence (Explicit)

an=a1+(n−1)da_n=a_1+(n-1)d

"a_n" represents the nth term in the sequence. "d" represents the common difference in an arithmetic sequence.

Sequences

Geometric Sequence (Explicit)

an=a1⋅rn−1a_n=a_1\cdot r^{n-1}

"a_n" represents the nth term in the sequence. "r" represents the common ratio in a geometric sequence.

Quadratic Equations and Functions

Standard Form in Quadratic Equations

y=ax2+bx+cy=ax^2+bx+c

Quadratic Equations and Functions

Vertex Form

y=a(x−h)2+ky=a(x-h)^2+k

Vertex: (h,k)

Quadratic Equations and Functions

Quadratic Formula

x=−b±b2−4ac2ax=\frac{-b\pm \sqrt{b^2-4ac}}{2a}

a, b, c refer to the a, b, c in the standard form of a quadratic equation.

Quadratic Equations and Functions

Axis of Symmetry

x=−b2ax=-\frac{b}{2a}

a, b refer to the a, b in the standard form of a quadratic equation.

Quadratic Equations and Functions

Discriminant

D=b2−4acD=b^2-4ac

a, b, c refer to the a, b, c in the standard form of a quadratic equation.

Applications of Algebra 1

Distance Formula

d=(x2−x1)2+(y2−y1)2d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

Allows you to find the distance between two points: (x1, y1) and (x2, y2).

Applications of Algebra 1

Midpoint Formula

M=(x1+x22,y1+y22)M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})

Allows you to find the midpoint between two points: (x1, y1) and (x2, y2).