The quadratic formula is a formula that is used to solve quadratic equations of the form ax^2 + bx + c = 0, where a, b, and c are constants and a ≠ 0.

The quadratic formula is given by:

x = (-b ± √(b² - 4ac)) / (2a)

When using the quadratic formula to solve a quadratic equation, follow these steps:

- Identify the values of a, b, and c in the quadratic equation ax^2 + bx + c = 0.
- Substitute the values of a, b, and c into the quadratic formula.
- Calculate the value of the discriminant (b² - 4ac) to determine the nature of the roots.
- If the discriminant is positive, there are two real and distinct roots; if it is zero, there is one real root (a repeated root); and if it is negative, there are two complex roots.
- Use the formula to calculate the values of x using the values of a, b, c, and the discriminant.
- Write the solutions in the form x = (-b ± √(b² - 4ac)) / (2a).

Solve the quadratic equation 2x^2 - 5x + 2 = 0 using the quadratic formula.

First, identify the values of a, b, and c:

a = 2, b = -5, c = 2

Substitute these values into the quadratic formula:

x = (-(-5) ± √((-5)² - 4(2)(2))) / (2*2)

Calculate the discriminant:

Discriminant = (-5)² - 4(2)(2) = 25 - 16 = 9 (positive)

Since the discriminant is positive, there are two real and distinct roots.

Calculate the values of x:

x = (-(-5) + √(9)) / (4) = (5 + 3) / 4 = 8/4 = 2

x = (-(-5) - √(9)) / (4) = (5 - 3) / 4 = 2/4 = 1/2

Therefore, the solutions are x = 2 and x = 1/2.

Now that you have a good understanding of the quadratic formula, you can practice solving quadratic equations using this method. Good luck!

Study GuideAlgebraic Equations Worksheet/Answer key

Algebraic Equations Worksheet/Answer key

Algebraic Equations Worksheet/Answer key

Algebraic Equations Worksheet/Answer keyAlgebraic Equations Worksheet/Answer key

Algebraic Equations Worksheet/Answer keyAlgebraic Equations

Algebra (NCTM)

Represent and analyze mathematical situations and structures using algebraic symbols.

Recognize and generate equivalent forms for simple algebraic expressions and solve linear equations

Grade 6 Curriculum Focal Points (NCTM)

Algebra: Writing, interpreting, and using mathematical expressions and equations

Students write mathematical expressions and equations that correspond to given situations, they evaluate expressions, and they use expressions and formulas to solve problems. They understand that variables represent numbers whose exact values are not yet specified, and they use variables appropriately. Students understand that expressions in different forms can be equivalent, and they can rewrite an expression to represent a quantity in a different way (e.g., to make it more compact or to feature different information). Students know that the solutions of an equation are the values of the variables that make the equation true. They solve simple one-step equations by using number sense, properties of operations, and the idea of maintaining equality on both sides of an equation. They construct and analyze tables (e.g., to show quantities that are in equivalent ratios), and they use equations to describe simple relationships (such as 3x = y) shown in a table.