Square Root & Complete the Square

Front

What is the process to complete the square for a quadratic equation?

Back

1. Move the constant term to the other side of the equation. 2. Take half of the coefficient of the x term, square it, and add it to both sides. 3. Factor the left side and solve for x.

Front

How do you find the vertex of a parabola given in standard form?

Back

The vertex can be found using the formula (-b/2a, f(-b/2a)) where f(x) is the quadratic function.

Front

What is the formula for the square of a binomial?

Back

(a + b)² = a² + 2ab + b² and (a - b)² = a² - 2ab + b².

Front

What does it mean to take the square root of a number?

Back

Taking the square root of a number x means finding a number y such that y² = x.

Front

What are the solutions to the equation x² = k?

Back

The solutions are x = ±√k.

Front

How do you solve a quadratic equation using the square root method?

Back

Isolate the squared term on one side of the equation, then take the square root of both sides and solve for the variable.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b² - 4ac) determines the nature of the roots: if positive, two real roots; if zero, one real root; if negative, no real roots.

Front

What is the standard form of a quadratic equation?

Back

The standard form is ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

How do you convert a quadratic equation from standard form to vertex form?

Back

Use the method of completing the square to rewrite the equation in the form y = a(x - h)² + k, where (h, k) is the vertex.

Front

What is the relationship between the roots of a quadratic equation and its factors?

Back

If r1 and r2 are the roots, the quadratic can be factored as a(x - r1)(x - r2).