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 of a quadratic equation indicate?

Back

The discriminant (D = b² - 4ac) indicates the nature of the roots of the quadratic equation: D > 0 means 2 real solutions, D = 0 means 1 real solution, and D < 0 means no real solutions.

Front

Calculate the discriminant for the equation: 2x² + 3x + 1 = 0.

Back

D = b² - 4ac = 3² - 4(2)(1) = 9 - 8 = 1 (Positive, 2 solutions).

Front

What is the significance of a zero discriminant?

Back

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

Front

Solve the quadratic equation using the Quadratic Formula: x² - 4x + 4 = 0.

Back

x = (4 ± √(0)) / 2 = 2 (One solution, x = 2).

Front

What is the vertex form of a quadratic function?

Back

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

Front

How do you determine if a quadratic opens upwards or downwards?

Back

A quadratic opens upwards if the coefficient 'a' in ax² + bx + c is positive, and downwards if 'a' is negative.

Front

What is the axis of symmetry for the quadratic function y = 2x² + 4x + 1?

Back

The axis of symmetry is given by x = -b/(2a). For this function, x = -4/(2*2) = -1.

Front

What is the maximum or minimum value of a quadratic function?

Back

The maximum or minimum value occurs at the vertex. If 'a' is positive, it is a minimum; if 'a' is negative, it is a maximum.

Front

Solve the equation: 3x² - 12x + 12 = 0 using the Quadratic Formula.

Back

x = (12 ± √(0)) / 6 = 2 (One solution, x = 2).