Quadratic Formula & Discriminant

Front

What is the Quadratic Formula?

Back

The Quadratic Formula is used to find the solutions of a quadratic equation in the form ax² + bx + c = 0. It is given by x = (-b ± √(b² - 4ac)) / (2a).

Front

What does the Discriminant (D) represent in a quadratic equation?

Back

The Discriminant (D = b² - 4ac) determines the number and type of solutions of a quadratic equation. If D > 0, there are two distinct real solutions; if D = 0, there is one real solution; if D < 0, there are no real solutions.

Front

Solve using the Quadratic Formula: 2x² - 9x - 35 = 0

Back

x = -5/2, x = 7

Front

Solve using the Quadratic Formula: 2x² + 2x - 12 = 0

Back

x = 2, x = -3

Front

What are the zeros of the equation (x + 10)(x - 2) = 0?

Back

The zeros are x = -10 and x = 2.

Front

If the Discriminant is -7, how many solutions does the quadratic equation have?

Back

The quadratic equation has no real solutions.

Front

What is the significance of a positive Discriminant?

Back

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

Front

What is the significance of a Discriminant equal to zero?

Back

A Discriminant equal to zero indicates that the quadratic equation has exactly one real solution (a repeated root).

Front

What is the significance of a negative Discriminant?

Back

A negative Discriminant indicates that the quadratic equation has no real solutions, only complex solutions.

Front

What is the vertex form of a quadratic equation?

Back

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