Completing the Square and Discriminant

Front

What does a discriminant of 0 indicate about the x-intercepts of a quadratic function?

Back

It indicates that the quadratic function has exactly 1 x-intercept.

Front

How do you calculate the discriminant of a quadratic equation in the form ax² + bx + c?

Back

The discriminant is calculated using the formula b² - 4ac.

Front

What is the nature of the solutions if the discriminant is positive?

Back

If the discriminant is positive, the quadratic equation has 2 distinct real solutions.

Front

What is the nature of the solutions if the discriminant is negative?

Back

If the discriminant is negative, the quadratic equation has 2 complex (imaginary) solutions.

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.

Front

Is x² + 6x + 9 a perfect square trinomial?

Back

Yes, it can be factored as (x + 3)².

Front

How do you complete the square for the expression x² + 6x?

Back

To complete the square, add (6/2)² = 9, resulting in (x + 3)².

Front

What is the missing value to complete the square for x² + 6x + ____?

Back

The missing value is 9.

Front

What is the discriminant of the quadratic equation x² + 2x - 63?

Back

The discriminant is 256.

Front

What does a discriminant of 256 indicate about the solutions of the equation x² + 2x - 63?

Back

It indicates that there are 2 distinct real solutions that are rational.