Solving Quadratic Equations Flashcard #6 Review

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of degree 2, typically in the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What are the methods to solve quadratic equations?

Back

The methods to solve quadratic equations include factoring, using the quadratic formula, completing the square, and graphing.

Front

What is the quadratic formula?

Back

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

Front

What does it mean to complete the square?

Back

Completing the square is a method used to convert a quadratic equation into a perfect square trinomial, making it easier to solve.

Front

How do you solve 3x² - 48 = 0 using the square root method?

Back

First, isolate x²: 3x² = 48. Then divide by 3: x² = 16. Finally, take the square root: x = ±4.

Front

What are the roots of the equation x² - 6x + 9 = 0?

Back

The roots are x = 3, found by factoring (x - 3)² = 0.

Front

What is the vertex of a parabola represented by the equation y = ax² + bx + c?

Back

The vertex can be found using the formula (-b/(2a), f(-b/(2a))) where f is the function.

Front

What does the discriminant tell us about the roots of a quadratic equation?

Back

The discriminant (b² - 4ac) indicates the nature of the roots: if > 0, two real roots; if = 0, one real root; if < 0, no real roots.

Front

How do you determine if a quadratic equation has no solution?

Back

A quadratic equation has no solution if its discriminant is less than zero (b² - 4ac < 0).

Front

What is the significance of the x-intercepts of a quadratic function?

Back

The x-intercepts are the points where the graph of the quadratic function crosses the x-axis, representing the roots of the equation.