Discriminant

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 of the equation.

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, but two complex solutions.

Front

How do you find the values of a, b, and c in a quadratic equation?

Back

In the standard form ax² + bx + c = 0, a is the coefficient of x², b is the coefficient of x, and c is the constant term.

Front

Given the equation 4x² - 8x - 3 = 0, what are the values of a, b, and c?

Back

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

Front

What is the formula to find the roots of a quadratic equation?

Back

The roots can be found using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).

Front

What is the axis of symmetry in a quadratic function?

Back

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

Front

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

Back

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

Front

What is the significance of the y-intercept in a quadratic equation?

Back

The y-intercept is the point where the graph intersects the y-axis, found by evaluating the function at x = 0.