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 do the coefficients A, B, and C represent in a quadratic equation?

Back

In the quadratic equation ax² + bx + c = 0, A is the coefficient of x², B is the coefficient of x, and C is the constant term.

Front

How do you identify A, B, and C from the equation 11r² + 6r = 6?

Back

Rearranging the equation to standard form gives 11r² + 6r - 6 = 0. Thus, A=11, B=6, C=-6.

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

How do you apply the Quadratic Formula to solve 4v² - 1v - 18 = 0?

Back

Identify A=4, B=-1, C=-18. Then, substitute into the formula: v = (1 ± √((-1)² - 4(4)(-18))) / (2(4)). This gives v = 2.25 and v = -2.

Front

What is the discriminant in the Quadratic Formula?

Back

The discriminant is the part of the formula under the square root: b² - 4ac. 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 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 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.

Front

How do you rearrange the equation 3m² - 14 = 11m into standard form?

Back

Rearranging gives 3m² - 11m - 14 = 0, where A=3, B=-11, C=-14.