Solving Quadratic Equations

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0.

Front

What is the discriminant in a quadratic equation?

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 it mean if the discriminant is positive?

Back

If the discriminant is positive, the quadratic equation has two distinct real solutions.

Front

What does it mean if the discriminant is zero?

Back

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

Front

What does it mean if the discriminant is negative?

Back

If the discriminant is negative, the quadratic equation has no real solutions (the solutions are complex).

Front

How do you solve a quadratic equation by taking square roots?

Back

To solve by taking square roots, isolate x² on one side and then take the square root of both sides, remembering to consider both the positive and negative roots.

Front

What is completing the square?

Back

Completing the square is a method used to solve quadratic equations by rewriting the equation in the form (x - p)² = q.

Front

How do you complete the square for the equation x² - 8x + ___?

Back

To complete the square, take half of the coefficient of x (which is -8), square it (16), and add it to the equation.

Front

What is the square root method for solving quadratic equations?

Back

The square root method involves isolating x² and then taking the square root of both sides to find the values of x.