Quadratic Formula and Discriminant

Front

What is the Quadratic Formula?

Back

x = (-b ± √(b² - 4ac)) / (2a)

Front

What is the Discriminant?

Back

The Discriminant is given by the formula b² - 4ac.

Front

What does a positive Discriminant indicate about the roots of a quadratic equation?

Back

It indicates that there are two distinct real solutions.

Front

What does a Discriminant of zero indicate?

Back

It indicates that there is exactly one real solution (a repeated root).

Front

What does a negative Discriminant indicate?

Back

It indicates that there are no real solutions (the solutions are complex).

Front

How do you determine the number of roots from the Discriminant?

Back

If b² - 4ac > 0, there are 2 roots; if b² - 4ac = 0, there is 1 root; if b² - 4ac < 0, there are no real roots.

Front

What is the vertex of a parabola represented by a quadratic equation?

Back

The vertex is the point (h, k) where h = -b/(2a) and k is the value of the quadratic function at h.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is the vertical line x = -b/(2a).

Front

How can you use the Quadratic Formula to solve x² + 4x - 40 = -8?

Back

Rearrange to x² + 4x - 32 = 0, then apply the Quadratic Formula to find x = -8 and x = 4.

Front

What is the significance of the coefficients a, b, and c in a quadratic equation?

Back

a determines the direction and width of the parabola, b affects the position of the vertex, and c is the y-intercept.