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Algebra 1Algebra 1293 views·Updated Jun 1, 2026·4 pages

Understanding Math Functions

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Ari@ari_beauty.17

Math formulas are the essential building blocks you need to... Show more

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# Formulas * distance point $\rightarrow \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$ * midpoint $((x_1+x_2)/2), ((y_1+y_2)/2)$ * Slope $(y_2-y_

Essential Math Formulas

Ever wonder how to find the distance between two points or figure out a parabola's vertex? These formulas are your toolkit for solving coordinate geometry and algebra problems.

The distance formula helps you find how far apart two points are: √(x2−x1)2+(y2−y1)2(x₂-x₁)²+(y₂-y₁)². When you need the point exactly between two locations, use the midpoint formula: (x1+x2)/2,(y1+y2)/2(x₁+x₂)/2, (y₁+y₂)/2.

For lines, the slope formula rise/runrise/run is y2−y1y₂-y₁/x2−x1x₂-x₁. You can write equations using point-slope form y−y1=m(x−x1)y-y₁=m(x-x₁) or the simpler slope-intercept form y=mx+by=mx+b. When dealing with parabolas, the quadratic formula −b±√(b2−4ac)-b±√(b²-4ac)/2a solves for the x-intercepts of y=ax²+bx+c.

Pro Tip: To find where a parabola reaches its highest or lowest point (the vertex), use x=-b/2a, then plug that x-value into the original equation to find y.

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of 4
# Formulas * distance point $\rightarrow \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$ * midpoint $((x_1+x_2)/2), ((y_1+y_2)/2)$ * Slope $(y_2-y_

Area and Perimeter Formulas

Need to calculate how much fencing for a yard or paint for a wall? These formulas will help you find the space inside (area) and distance around (perimeter) different shapes.

For squares and rectangles, area is straightforward: square area is s² (side squared), while rectangle area is l×w (length times width). Triangle area is ½(b×h) – half the base times the height. For circles, area equals πr² (pi times radius squared).

When calculating perimeters, square perimeter equals 4s (four sides), rectangle perimeter is 2l+2w (twice length plus twice width), and triangle perimeter is the sum of all three sides. The distance around a circle, called circumference, equals 2πr.

Remember: For irregular shapes like trapezoids area=h(b1+b2)/2area = h(b₁+b₂)/2, break them down into simpler shapes you already know how to calculate!

3
of 4
# Formulas * distance point $\rightarrow \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$ * midpoint $((x_1+x_2)/2), ((y_1+y_2)/2)$ * Slope $(y_2-y_

Volume and Surface Area

When you jump into 3D shapes, you'll need formulas to find how much space is inside (volume) and how much material covers the outside (surface area).

A sphere's volume is (4/3)πr³, while a cone's volume is (1/3)πr²h. For containers like cylinders, volume equals πr²h, and a rectangular prism's volume is simply l×w×h (length × width × height).

Surface area calculations help you determine how much wrapping paper you'd need for a box or paint for a tank. A sphere's surface area is 4πr², a cylinder's surface area is 2πrh+2πr² (curved side plus two circular ends), and a rectangular prism's surface area is 2wl+hl+hwwl+hl+hw.

Visualization Tip: Think of volume as how many cubes fit inside a shape, while surface area is like unfolding the shape and measuring its "skin."

4
of 4
# Formulas * distance point $\rightarrow \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$ * midpoint $((x_1+x_2)/2), ((y_1+y_2)/2)$ * Slope $(y_2-y_

Logarithmic and Exponential Formulas

Logarithms and exponentials might seem tricky at first, but they're super useful for problems involving growth, decay, and solving certain equations.

The log product rule loga(P⋅Q)=logaP+logaQlogₐ(P·Q) = logₐP + logₐQ lets you split a logarithm of multiplied numbers. When dividing inside a logarithm, use the log quotient rule: logₐP/QP/Q = logₐP - logₐQ. For exponents inside logarithms, the log power rule states logₐPqP^q = q·logₐP.

With exponentials, remember that multiplying the same base with different exponents means you add the exponents: a^m·a^n = a^m+nm+n. When dividing exponentials with the same base, subtract the exponents: a^m/a^n = a^m−nm-n.

Real-World Connection: These formulas are crucial for understanding compound interest, population growth, and radioactive decay. For example, the amount in a bank account with compound interest can be calculated using P1+r/n1+r/n^(nt).

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Algebra 1Algebra 1293 views·Updated Jun 1, 2026·4 pages

Understanding Math Functions

user profile picture
Ari@ari_beauty.17

Math formulas are the essential building blocks you need to solve problems across different areas of mathematics. This guide provides key formulas for geometry, algebra, and more that will help you solve problems quickly and accurately.

1
of 4
# Formulas * distance point $\rightarrow \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$ * midpoint $((x_1+x_2)/2), ((y_1+y_2)/2)$ * Slope $(y_2-y_

Sign up to see the content. It's free!

  • Access to all documents
  • Improve your grades
  • Join milions of students

Essential Math Formulas

Ever wonder how to find the distance between two points or figure out a parabola's vertex? These formulas are your toolkit for solving coordinate geometry and algebra problems.

The distance formula helps you find how far apart two points are: √(x2−x1)2+(y2−y1)2(x₂-x₁)²+(y₂-y₁)². When you need the point exactly between two locations, use the midpoint formula: (x1+x2)/2,(y1+y2)/2(x₁+x₂)/2, (y₁+y₂)/2.

For lines, the slope formula rise/runrise/run is y2−y1y₂-y₁/x2−x1x₂-x₁. You can write equations using point-slope form y−y1=m(x−x1)y-y₁=m(x-x₁) or the simpler slope-intercept form y=mx+by=mx+b. When dealing with parabolas, the quadratic formula −b±√(b2−4ac)-b±√(b²-4ac)/2a solves for the x-intercepts of y=ax²+bx+c.

Pro Tip: To find where a parabola reaches its highest or lowest point (the vertex), use x=-b/2a, then plug that x-value into the original equation to find y.

2
of 4
# Formulas * distance point $\rightarrow \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$ * midpoint $((x_1+x_2)/2), ((y_1+y_2)/2)$ * Slope $(y_2-y_

Sign up to see the content. It's free!

  • Access to all documents
  • Improve your grades
  • Join milions of students

Area and Perimeter Formulas

Need to calculate how much fencing for a yard or paint for a wall? These formulas will help you find the space inside (area) and distance around (perimeter) different shapes.

For squares and rectangles, area is straightforward: square area is s² (side squared), while rectangle area is l×w (length times width). Triangle area is ½(b×h) – half the base times the height. For circles, area equals πr² (pi times radius squared).

When calculating perimeters, square perimeter equals 4s (four sides), rectangle perimeter is 2l+2w (twice length plus twice width), and triangle perimeter is the sum of all three sides. The distance around a circle, called circumference, equals 2πr.

Remember: For irregular shapes like trapezoids area=h(b1+b2)/2area = h(b₁+b₂)/2, break them down into simpler shapes you already know how to calculate!

3
of 4
# Formulas * distance point $\rightarrow \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$ * midpoint $((x_1+x_2)/2), ((y_1+y_2)/2)$ * Slope $(y_2-y_

Sign up to see the content. It's free!

  • Access to all documents
  • Improve your grades
  • Join milions of students

Volume and Surface Area

When you jump into 3D shapes, you'll need formulas to find how much space is inside (volume) and how much material covers the outside (surface area).

A sphere's volume is (4/3)πr³, while a cone's volume is (1/3)πr²h. For containers like cylinders, volume equals πr²h, and a rectangular prism's volume is simply l×w×h (length × width × height).

Surface area calculations help you determine how much wrapping paper you'd need for a box or paint for a tank. A sphere's surface area is 4πr², a cylinder's surface area is 2πrh+2πr² (curved side plus two circular ends), and a rectangular prism's surface area is 2wl+hl+hwwl+hl+hw.

Visualization Tip: Think of volume as how many cubes fit inside a shape, while surface area is like unfolding the shape and measuring its "skin."

4
of 4
# Formulas * distance point $\rightarrow \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$ * midpoint $((x_1+x_2)/2), ((y_1+y_2)/2)$ * Slope $(y_2-y_

Sign up to see the content. It's free!

  • Access to all documents
  • Improve your grades
  • Join milions of students

Logarithmic and Exponential Formulas

Logarithms and exponentials might seem tricky at first, but they're super useful for problems involving growth, decay, and solving certain equations.

The log product rule loga(P⋅Q)=logaP+logaQlogₐ(P·Q) = logₐP + logₐQ lets you split a logarithm of multiplied numbers. When dividing inside a logarithm, use the log quotient rule: logₐP/QP/Q = logₐP - logₐQ. For exponents inside logarithms, the log power rule states logₐPqP^q = q·logₐP.

With exponentials, remember that multiplying the same base with different exponents means you add the exponents: a^m·a^n = a^m+nm+n. When dividing exponentials with the same base, subtract the exponents: a^m/a^n = a^m−nm-n.

Real-World Connection: These formulas are crucial for understanding compound interest, population growth, and radioactive decay. For example, the amount in a bank account with compound interest can be calculated using P1+r/n1+r/n^(nt).

We thought you’d never ask...

What is the Knowunity AI companion?

Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.

Where can I download the Knowunity app?

You can download the app in the Google Play Store and in the Apple App Store.

Is Knowunity really free of charge?

That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.

Most popular content: Volume Formulas

1

Most popular content in Algebra 1

9

Most popular content

9

Can't find what you're looking for? Explore other subjects.

Students love us — and so will you.

4.6/5App Store
4.7/5Google Play

The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.

Stefan SiOS user

This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.

Samantha KlichAndroid user

Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.

AnnaiOS user