Discriminant and Vertex Form Review

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is a value calculated from the coefficients of a quadratic equation in the form ax² + bx + c. It is given by the formula D = b² - 4ac and determines the nature of the roots.

Front

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

Back

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

Front

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

Back

A negative discriminant indicates that the quadratic equation has two complex (non-real) solutions.

Front

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

Back

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

Front

How do you find the vertex of a parabola in vertex form?

Back

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

Front

What is the vertex of the parabola given by the equation y = 2(x-3)² + 4?

Back

The vertex of the parabola is (3, 4).

Front

What is the leading coefficient in the quadratic equation y = ax² + bx + c?

Back

The leading coefficient is the coefficient 'a' in the quadratic equation, which determines the direction of the parabola's opening.

Front

In the equation y = x² + 5x + 7, what are the values of a, b, and c?

Back

In the equation y = x² + 5x + 7, a = 1, b = 5, and c = 7.

Front

How do you calculate the discriminant for the equation -2x² - x - 1 = 0?

Back

The discriminant is calculated using D = b² - 4ac. For -2x² - x - 1, a = -2, b = -1, c = -1. Thus, D = (-1)² - 4(-2)(-1) = 1 - 8 = -7.

Front

What is the significance of the vertex in a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on whether it opens upwards or downwards.