Quadratic Formula & 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

Identify the values of a, b, and c in the equation 4x² - 8x - 3 = 0.

Back

a = 4, b = -8, c = -3.

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 the quadratic equation.

Front

If the discriminant is positive, what can we conclude about the solutions?

Back

There are two distinct real solutions.

Front

If the discriminant is zero, what can we conclude about the solutions?

Back

There is exactly one real solution (a repeated root).

Front

If the discriminant is negative, what can we conclude about the solutions?

Back

There are no real solutions (the solutions are complex).

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex represents the maximum or minimum point of the parabola.

Front

How do you find the axis of symmetry of a quadratic function?

Back

The axis of symmetry can be found using the formula x = -b / (2a).

Front

What is the standard form of a quadratic equation?

Back

The standard form is ax² + bx + c = 0, where a, b, and c are constants.

Front

What is the vertex form of a quadratic equation?

Back

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