Front

What is the discriminant in a quadratic equation?

Back

The discriminant is a value calculated from the coefficients of a quadratic equation in the form ax² + bx + c. It is given by the formula D = b² - 4ac. The discriminant determines the nature of the roots of the quadratic equation.

Front

Calculate the discriminant of the equation -2x² - x - 1 = 0.

Back

D = (-1)² - 4(-2)(-1) = 1 - 8 = -7.

Front

What are the solutions to the equation 4m² - 100 = 0?

Back

m = 5 and m = -5.

Front

How do you solve a quadratic equation by taking square roots?

Back

To solve a quadratic equation by taking square roots, isolate the x² term, then take the square root of both sides, remembering to consider both the positive and negative roots.

Front

Find the zeros of the quadratic function represented by the equation x² + 4x = 0.

Back

The zeros are x = 0 and x = -4.

Front

What is a zero of a quadratic function?

Back

A zero of a quadratic function is a value of x that makes the function equal to zero. It represents the x-intercepts of the graph of the function.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola represented by the quadratic function. It 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 does it mean if the discriminant is positive?

Back

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

Front

What does it mean if the discriminant is zero?

Back

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