Quadratic Formula

Front

What is the standard form of a quadratic equation?

Back

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

Front

What does the leading coefficient in a quadratic equation represent?

Back

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

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the expression b^2 - 4ac, which determines the nature of the roots of the quadratic equation.

Front

How do you calculate the discriminant for the equation x^2 + 3x - 4 = 0?

Back

For the equation x^2 + 3x - 4, a = 1, b = 3, c = -4. The discriminant is calculated as 3^2 - 4(1)(-4) = 9 + 16 = 25.

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 (the roots are complex or imaginary).

Front

What are the roots of the equation x^2 + 4x + 3 = 0?

Back

The roots of the equation x^2 + 4x + 3 = 0 are x = -1 and x = -3.

Front

How do you solve the equation x^2 + 2x - 1 = 2?

Back

First, rearrange to x^2 + 2x - 3 = 0. Then, factor or use the quadratic formula to find the roots: x = 1 and x = -3.

Front

What is the quadratic formula used to find the roots of a quadratic equation?

Back

The quadratic formula is x = (-b ± √(b^2 - 4ac)) / (2a).