Quadratic Formula & Discriminant

Front

What is the Quadratic Formula?

Back

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

Front

What does the Discriminant indicate in a quadratic equation?

Back

The Discriminant (D = b² - 4ac) indicates the nature of the roots of a quadratic equation. If D > 0, there are 2 distinct real solutions; if D = 0, there is 1 real solution; if D < 0, there are 2 complex (imaginary) solutions.

Front

If the Discriminant is zero, what can be said about the roots of the quadratic equation?

Back

If the Discriminant is zero, the quadratic equation has exactly one real solution (a repeated root).

Front

How do you identify a, b, and c in the quadratic equation 4x² - 8x = 3?

Back

Rearranging to standard form gives 4x² - 8x - 3 = 0. Here, a = 4, b = -8, c = -3.

Front

Solve the quadratic equation 2x² + 2x - 12 = 0 using the quadratic formula.

Back

Using the quadratic formula, the solutions are x = 2 and x = -3.

Front

What happens if the Discriminant is negative?

Back

If the Discriminant is negative, the quadratic equation has 2 complex (imaginary) solutions.

Front

Can the quadratic formula be used for equations that can be factored?

Back

Yes, the quadratic formula can be used for both factorable and non-factorable quadratic equations.

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 is the vertex of a parabola represented by a quadratic equation?

Back

The vertex of a parabola represented by the quadratic equation y = ax² + bx + c can be found using the formula (-b/(2a), f(-b/(2a))).

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry of a quadratic function in standard form y = ax² + bx + c is the vertical line x = -b/(2a).