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 and a ≠ 0.

Front

What does the 'a' value represent in a quadratic equation?

Back

The 'a' value represents the coefficient of x² and determines the direction of the parabola (upward if a > 0, downward if a < 0).

Front

What does the 'b' value represent in a quadratic equation?

Back

The 'b' value is the coefficient of x and affects the position of the vertex of the parabola along the x-axis.

Front

What does the 'c' value represent in a quadratic equation?

Back

The 'c' value is the constant term and represents the y-intercept of the quadratic function.

Front

How do you identify the coefficients a, b, and c in the equation 4x² - 8x = 3?

Back

Rearranging the equation to standard form gives 4x² - 8x - 3 = 0, so a = 4, b = -8, c = -3.

Front

What is the quadratic formula?

Back

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

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, which determines the nature of the roots.

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).

Front

What does it mean if the discriminant is negative?

Back

If the discriminant is negative, the quadratic equation has no real roots, but two complex roots.