📆 Updated: 1 Jan 1970
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Algebra worksheets are essential learning tools that offer an organized and comprehensive approach to mastering concepts in 8th Grade Algebra. These worksheets are specifically designed to support students in understanding and applying mathematical principles related to variables, equations, graphs, functions, and more. With structured exercises and a wide range of problem-solving opportunities, these worksheets provide an excellent resource for 8th graders seeking to strengthen their algebraic foundation.

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### What is the quadratic formula?

The quadratic formula is used to find the solutions to a quadratic equation of the form ax^2 + bx + c = 0, where a, b, and c are constants and a ? 0. The formula is x = (-b ± ?(b^2 - 4ac)) / 2a.

### How do you solve a system of equations using substitution?

To solve a system of equations using substitution, you first isolate one of the variables in one of the equations. Then, substitute this expression into the other equation to solve for the other variable. Once you have found the value of one variable, substitute it back into either of the original equations to find the value of the other variable. This process allows you to find the unique solution where the two equations intersect.

### What is the slope-intercept form of a linear equation?

The slope-intercept form of a linear equation is y = mx + b, where m represents the slope of the line and b represents the y-intercept, which is the value of y when x = 0. This form allows us to easily identify the slope and y-intercept of a linear equation and graph the line on a coordinate plane.

### How do you simplify radicals?

To simplify radicals, you need to factor the number inside the square root sign and find the largest perfect square that divides evenly into it. Then, you can separate the perfect square factor from the rest of the number to simplify the radical expression. Repeat this process until the number inside the square root sign is a prime number or can no longer be simplified further. Remember to simplify the expression by multiplying any constants outside the square root with the simplified radical.

### What is the exponent rule for multiplying powers with the same base?

When multiplying powers with the same base, you can add the exponents together. This rule is expressed as (a^m) x (a^n) = a^(m+n), where "a" is the base, and "m" and "n" are the exponents of the powers being multiplied.

### How do you graph a linear inequality on a number line?

To graph a linear inequality on a number line, you begin by treating the inequality as if it is an equation and graph the line accordingly. If the inequality is < or >, the line drawn is dashed. If the inequality is ? or ?, the line drawn is solid. Then, you determine which side of the line to shade based on the inequality sign: if it is > or ?, shade above the line; if it is < or ?, shade below the line. Remember to use open or closed dots at the endpoint of the line to indicate if it includes that value in the solution set or not.

### How do you find the domain and range of a function?

To find the domain of a function, identify all possible input values that the function can accept without resulting in any undefined operations. The domain represents the set of all possible x-values. To find the range, determine all possible output values that the function can generate based on the given domain. The range represents the set of all possible y-values. Analyzing the behavior of the function's graph or transforming the function can also help in determining the domain and range.

### What is the difference between an expression and an equation?

An expression is a mathematical phrase that can contain numbers, variables, and operations, but it does not have an equal sign. It is a representation of a value. On the other hand, an equation is a mathematical statement that contains an equal sign and shows that two expressions are equal to each other. Equations are used to solve for unknown variables by finding the value that satisfies the equality.

### How do you solve a literal equation for a specific variable?

To solve a literal equation for a specific variable, isolate the variable of interest by using inverse operations to move all other terms to the other side of the equation. Perform operations in the reverse order of the original equation to ensure accurate and equivalent transformations. Once the variable is isolated, the equation will be in a form where the desired variable is expressed alone and solved for.

### What is the Pythagorean theorem and how is it used to find the length of a side in a right triangle?

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This theorem is represented by the formula a^2 + b^2 = c^2, where a and b are the lengths of the two shorter sides (legs) and c is the length of the hypotenuse. To find the length of a side in a right triangle using the Pythagorean theorem, you simply need to substitute the known values into the formula and solve for the unknown side length.

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