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 (x - p)² = q, where p and q are constants. This method helps in solving quadratic equations and understanding their graph.

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is a quadratic expression that can be factored into the square of a binomial, such as x² - 4x + 4 = (x - 2)².

Front

How do you identify the value to complete the square for the expression x² - 4x?

Back

To complete the square, take half of the coefficient of x (which is -4), square it, and add it to the expression. Half of -4 is -2, and (-2)² = 4.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

How do you convert the equation x² - 4x + 4 = 20 into vertex form?

Back

First, move 20 to the left side: x² - 4x + 4 - 20 = 0, which simplifies to (x - 2)² - 16 = 0. Thus, the vertex form is (x - 2)² = 16.

Front

What is the vertex of the parabola represented by the equation y = (x - 2)² - 16?

Back

The vertex of the parabola is the point (2, -16). This is derived from the vertex form of the equation.

Front

What does the term 'discriminant' refer to in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root, given by b² - 4ac. It determines the nature of the roots of the quadratic equation.

Front

What does a positive discriminant indicate about the roots of a quadratic equation?

Back

A positive discriminant indicates that the quadratic equation has two distinct real roots.

Front

What does a zero discriminant indicate about the roots of a quadratic equation?

Back

A zero discriminant indicates that the quadratic equation has exactly one real root, also known as a repeated or double root.

Front

What does a negative discriminant indicate about the roots of a quadratic equation?

Back

A negative discriminant indicates that the quadratic equation has no real roots, but two complex roots.