Warm up 2.13: Solving Quadratics by Square Roots

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 does it mean to solve a quadratic equation by square roots?

Back

Solving a quadratic equation by square roots involves isolating the squared term and taking the square root of both sides to find the variable's value.

Front

What is the square root of a number?

Back

The square root of a number x is a value y such that y² = x. For example, the square root of 9 is 3.

Front

How do you simplify √(a²)?

Back

√(a²) simplifies to |a|, which is the absolute value of a.

Front

What is the solution to (h - 2)² = 0?

Back

The solution is h = 2.

Front

What happens when you take the square root of a negative number?

Back

Taking the square root of a negative number results in an imaginary number, expressed as i√|x|.

Front

What is the value of √9?

Back

The value of √9 is 3.

Front

How do you solve x² = 16 using square roots?

Back

To solve x² = 16, take the square root of both sides: x = ±4.

Front

What is the principle of 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

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.