Quadratic Formula

Front

What is the Quadratic Formula?

Back

The Quadratic Formula is used to find the solutions (roots) of a quadratic equation in the form ax² + bx + c = 0. It is given by x = (-b ± √(b² - 4ac)) / (2a).

Front

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

Back

'a' represents the coefficient of x², which determines the direction and width of the parabola.

Front

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

Back

'b' represents the coefficient of x, which affects the position of the vertex of the parabola.

Front

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

Back

'c' represents the constant term, which is the y-intercept of the parabola.

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. It determines the nature of the roots.

Front

What does a positive discriminant indicate?

Back

A positive discriminant indicates that there are two distinct real roots.

Front

What does a zero discriminant indicate?

Back

A zero discriminant indicates that there is exactly one real root (a repeated root).

Front

What does a negative discriminant indicate?

Back

A negative discriminant indicates that there are no real roots, only complex roots.

Front

Solve for x: 2x² - 8x - 24 = 0

Back

x = 6, -2

Front

Find the value of x using the quadratic formula, if a=1, b=-5, and c=-14.

Back

x = 7, -2