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 nature of the roots of the quadratic equation. It indicates whether there are two real solutions, one real solution, or no real solutions.

Front

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

Back

If the discriminant is positive, there are two distinct real solutions.

Front

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

Back

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

Front

What does it mean if the discriminant is negative?

Back

If the discriminant is negative, there are no real solutions; the solutions are complex or imaginary.

Front

How can you determine if a parabola opens upwards or downwards?

Back

A parabola opens upwards if the coefficient of x² (a) is positive, and it opens downwards if a is negative.

Front

What are the zeros of a quadratic equation?

Back

The zeros of a quadratic equation are the values of x that make the equation equal to zero; they are the x-intercepts of the graph.

Front

How do you find the zeros of the equation (x + 10)(x - 2) = 0?

Back

Set each factor to zero: x + 10 = 0 gives x = -10, and x - 2 = 0 gives x = 2. Thus, the zeros are -10 and 2.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on whether it opens upwards or downwards.

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. It can be found using the formula x = -b/(2a).