solve quadratic equations by finding 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 finding square roots?

Back

It means to isolate the variable by taking the square root of both sides of the equation, often resulting in two possible solutions.

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.

Front

How do you solve the equation -5x² = -50?

Back

Divide both sides by -5 to get x² = 10, then take the square root: x = ±√10.

Front

What are the solutions to the equation (x - 2)² = 49?

Back

x = 2 ± 7, which gives x = 9 and x = -5.

Front

How do you solve x² - 49 = 0?

Back

Factor the equation as (x - 7)(x + 7) = 0, giving solutions x = 7 and x = -7.

Front

What is the principle of taking square roots in solving equations?

Back

The principle states that if x² = a, then x = ±√a.

Front

How do you solve (x + 2)² = 25?

Back

Take the square root of both sides: x + 2 = ±5, leading to x = 3 and x = -7.

Front

What is the importance of the ± symbol in square root solutions?

Back

The ± symbol indicates that there are two possible solutions: one positive and one negative.

Front

What is the vertex form of a quadratic equation?

Back

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