Quadratic formula and discriminant

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the solutions of a quadratic equation ax² + bx + c = 0.

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root, given by b² - 4ac, which determines the nature of the roots.

Front

What does a positive discriminant indicate?

Back

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

Front

What does a zero discriminant indicate?

Back

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

Front

What does a negative discriminant indicate?

Back

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

Front

Calculate the discriminant for the equation 3x² + 4x + 1 = 0.

Back

The discriminant is 4² - 4(3)(1) = 16 - 12 = 4 (positive, two distinct real solutions).

Front

Calculate the discriminant for the equation x² - 6x + 9 = 0.

Back

The discriminant is (-6)² - 4(1)(9) = 36 - 36 = 0 (one real solution).

Front

Calculate the discriminant for the equation 2x² + 3x + 5 = 0.

Back

The discriminant is 3² - 4(2)(5) = 9 - 40 = -31 (negative, no real solutions).

Front

What is the significance of the axis of symmetry in a quadratic function?

Back

The axis of symmetry is the vertical line that divides the parabola into two mirror-image halves, given by x = -b/(2a).

Front

How do you determine the vertex of a quadratic function?

Back

The vertex can be found using the formula (h, k) where h = -b/(2a) and k = f(h).