Solving Equations (Linear and Quadratic)

Front

What is a linear equation?

Back

An equation that makes a straight line when graphed, typically in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is a quadratic equation?

Back

An equation that can be expressed in the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

How do you determine the degree of a polynomial?

Back

The degree of a polynomial is the highest exponent of the variable in the equation.

Front

What is the first step in solving the equation x² + 6x - 13 = 3?

Back

Make it equal 0 by subtracting 3 from both sides, resulting in x² + 6x - 16 = 0.

Front

How do you solve the equation 7x - 3x - 8 = 24?

Back

Combine like terms to get 4x - 8 = 24, then add 8 to both sides and divide by 4 to find x = 8.

Front

What does it mean to factor an equation?

Back

To express the equation as a product of its factors, which can help in finding the roots or solutions.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the solutions of a quadratic equation.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b² - 4ac) determines the nature of the roots: if positive, there are two real roots; if zero, one real root; if negative, no real roots.

Front

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

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you isolate a variable in an equation?

Back

By performing inverse operations to both sides of the equation until the variable is alone on one side.