Completing the Square and Discriminant

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is a quadratic expression that can be expressed as the square of a binomial, in the form (a + b)² = a² + 2ab + b².

Front

How do you find the missing value 'c' to complete the square for x² + bx + c?

Back

To find 'c', take half of 'b', square it, and add it to the expression. For example, for x² + 26x, (26/2)² = 169.

Front

What is the formula for the discriminant of a quadratic equation?

Back

The discriminant (D) is given by the formula D = b² - 4ac, where a, b, and c are coefficients in the quadratic equation ax² + bx + c = 0.

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 negative discriminant indicate about the roots of a quadratic equation?

Back

A negative discriminant indicates that the quadratic equation has no real roots, only complex 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

Factor the perfect square trinomial: x² + 16x + 64.

Back

(x + 8)².

Front

Complete the square for the expression x² + 12x + ___.

Back

The missing value is 36, so the complete expression is x² + 12x + 36.

Front

What is the vertex form of a quadratic function?

Back

The vertex form is y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

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

Back

To convert, complete the square on the quadratic expression.