Standard Form Calculator: Ax + By = C
This standard form calculator covers every meaning of standard form you meet in school. For a straight line, enter two points or the slope and y-intercept, and it writes the equation as Ax + By = C with whole-number coefficients and A positive. For a parabola, enter vertex form a(x - h)² + k and it expands to ax² + bx + c. For a number, it writes it in standard form, also called scientific notation (such as 4.5 × 10^6), and in expanded form (4,000,000 + 500,000). Each mode shows the slope or other key facts so you can check your work.
Standard Form Calculator
Write a line as Ax + By = C, a quadratic as ax² + bx + c, or a number in standard form.
How to use the Standard Form Calculator
- Choose a mode: line from two points, line from slope-intercept, quadratic, or number.
- Enter the values.
- Read the standard form answer and the steps.
Standard forms
Line: Ax + By = C with integers and A ≥ 0. Quadratic: ax² + bx + c. Number: a × 10^n with 1 ≤ |a| < 10.
Features
- Line through two points as Ax + By = C
- Slope-intercept to standard form
- Vertex form to ax² + bx + c
- Numbers in standard form (scientific notation)
- Expanded form of a number
- Whole-number coefficients
Frequently asked questions
What is the standard form of a linear equation?
Ax + By = C, where A, B and C are integers, A is not negative and the numbers share no common factor. For example, 2x + 3y = 6.
How do I convert y = mx + b to standard form?
Move the x term left: -mx + y = b, clear any decimals or fractions, then multiply by -1 if needed so A is positive. y = 2x + 3 becomes 2x - y = -3.
What is standard form of a quadratic?
ax² + bx + c. Vertex form 2(x - 1)² + 3 expands to 2x² - 4x + 5.
What is standard form for numbers?
In the UK and many textbooks it means scientific notation: a × 10^n with 1 ≤ a < 10. In US elementary math it can also mean writing a number with digits, the reverse of expanded form.
Why must A be positive?
It is a convention so every line has one agreed form, which makes answers easy to compare.