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 it mean if the discriminant (b² - 4ac) is positive?

Back

If the discriminant is positive, the quadratic equation has two distinct real solutions.

Front

What does it mean if the discriminant (b² - 4ac) is zero?

Back

If the discriminant is zero, the quadratic equation has exactly one real solution (a repeated root).

Front

What does it mean if the discriminant (b² - 4ac) is negative?

Back

If the discriminant is negative, the quadratic equation has no real solutions (the solutions are complex).

Front

How do you determine the vertex of a parabola represented by a quadratic equation?

Back

The vertex of a parabola given by y = ax² + bx + c can be found using the formula (-b/(2a), f(-b/(2a))).

Front

What is the standard form of a quadratic equation?

Back

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

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.

Front

What is the axis of symmetry in a quadratic function?

Back

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

Front

What is the range of a quadratic function that opens upwards?

Back

The range of a quadratic function that opens upwards is [k, ∞), where k is the y-coordinate of the vertex.

Front

What is the range of a quadratic function that opens downwards?

Back

The range of a quadratic function that opens downwards is (-∞, k], where k is the y-coordinate of the vertex.