Solving with Quadratic Formula

Front

What is the quadratic formula?

Back

The quadratic formula is used to find the solutions of a quadratic equation and is given by: x = (-b ± √(b² - 4ac)) / (2a).

Front

What does 'a' represent in the quadratic formula?

Back

'a' represents the coefficient of the x² term in a quadratic equation of the form ax² + bx + c = 0.

Front

What does 'b' represent in the quadratic formula?

Back

'b' represents the coefficient of the x term in a quadratic equation of the form ax² + bx + c = 0.

Front

What does 'c' represent in the quadratic formula?

Back

'c' represents the constant term in a quadratic equation of the form ax² + bx + c = 0.

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 for the quadratic equation.

Front

What does a zero discriminant indicate?

Back

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

Front

What does a negative discriminant indicate?

Back

A negative discriminant indicates that there are no real roots, but two complex roots for the quadratic equation.

Front

How do you apply the quadratic formula to the equation x² - 5x + 6 = 0?

Back

Using the quadratic formula: a=1, b=-5, c=6. The solutions are x = 2 and x = 3.

Front

What is the vertex form of a quadratic equation?

Back

The vertex form of a quadratic equation is y = a(x - h)² + k, where (h, k) is the vertex of the parabola.