Solving Quadratics by Completing the Square FLASHCARD

Front

What is the process of completing the square in a quadratic equation?

Back

Completing the square involves rewriting a quadratic equation in the form of a perfect square trinomial, allowing for easier solving and graphing.

Front

What is the standard form of a quadratic equation?

Back

Front

Back

Front

What is the vertex form of a quadratic equation?

Back

Front

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

Back

Front

How do you convert a quadratic equation from standard form to vertex form?

Back

To convert, complete the square on the quadratic expression and rearrange the equation.

Front

What is the formula for the vertex of a parabola given by a quadratic equation?

Back

Front

What does it mean for a quadratic equation to have complex roots?

Back

Complex roots occur when the discriminant is negative, indicating that the parabola does not intersect the x-axis.

Front

How do you solve a quadratic equation by completing the square?

Back

1. Move the constant to the other side. 2. Complete the square on the left side. 3. Solve for x by taking the square root.

Front

What is the relationship between the coefficients of a quadratic equation and its graph?

Back

The coefficients determine the shape, direction, and position of the parabola on the graph.