quadratic formula common formative

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants.

Front

How do you identify the coefficients a, b, and c in the equation 4x^2 + 8x = 9?

Back

In the equation 4x^2 + 8x - 9 = 0, a = 4, b = 8, and c = -9.

Front

What is the discriminant of a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root, given by b^2 - 4ac, which determines the nature of the roots.

Front

How do you calculate the discriminant for the equation 2x^2 - 5x - 3?

Back

For the equation 2x^2 - 5x - 3, the discriminant is calculated as (-5)^2 - 4(2)(-3) = 25 + 24 = 49.

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 solutions.

Front

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

Back

A discriminant of zero indicates that the quadratic equation has exactly one real solution (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 solutions, only complex solutions.

Front

Is the equation 3x^2 + 4x = 5 in standard form?

Back

No, the equation is not in standard form. It should be written as 3x^2 + 4x - 5 = 0.

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 ± √(b^2 - 4ac)) / (2a).

Front

What is the significance of the coefficient 'a' in a quadratic equation?

Back

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