Quadratic Formula

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.

Front

What does the 'a' represent in the quadratic equation ax² + bx + c = 0?

Back

The 'a' represents the leading coefficient, which determines the direction of the parabola (upward if a > 0, downward if a < 0).

Front

What does the 'b' represent in the quadratic equation ax² + bx + c = 0?

Back

The 'b' represents the coefficient of the linear term, which affects the position of the vertex of the parabola.

Front

What does the 'c' represent in the quadratic equation ax² + bx + c = 0?

Back

The 'c' represents the constant term, which is the y-intercept of the quadratic function.

Front

How do you convert a quadratic equation to standard form?

Back

To convert a quadratic equation to standard form, rearrange the equation so that one side equals zero, typically by moving all terms to one side.

Front

What is the quadratic formula used for?

Back

The quadratic formula is used to find the solutions (roots) of a quadratic equation and is given by x = (-b ± √(b² - 4ac)) / (2a).

Front

What is the discriminant in the quadratic formula?

Back

The discriminant is the part of the quadratic formula under the square root, b² - 4ac, and it determines the nature of the roots.

Front

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

Back

A positive discriminant indicates that the quadratic equation has two distinct real roots.

Front

What does a zero discriminant indicate about the roots of a quadratic equation?

Back

A zero discriminant indicates that the quadratic equation has exactly one real root (a repeated root).

Front

What does a negative discriminant indicate about the roots of a quadratic equation?

Back

A negative discriminant indicates that the quadratic equation has no real roots, but two complex roots.