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.

Tags

CCSS.HSA-REI.B.4B

Front

What does it mean if the discriminant is positive?

Back

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

Tags

CCSS.HSA-REI.B.4B

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).

Tags

CCSS.HSA-REI.B.4B

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).

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.HSA-REI.B.4B

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.

Tags

CCSS.HSA-REI.B.4B