Completing the square

Front

What is completing the square?

Back

Completing the square is a method used to convert a quadratic equation from standard form (ax^2 + bx + c) to vertex form (a(x-h)^2 + k), making it easier to analyze the properties of the quadratic function.

Front

What is the vertex form of a quadratic equation?

Back

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

Front

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

Back

In the vertex form y = a(x-h)^2 + k, the vertex is the point (h, k).

Front

What is the first step in completing the square for the equation y = x^2 + 14x + 50?

Back

Subtract 50 from both sides to isolate the quadratic expression: y - 50 = x^2 + 14x.

Front

What is the formula to complete the square for a quadratic expression?

Back

To complete the square for ax^2 + bx, use the formula: (b/2)^2. Add and subtract this value inside the equation.

Front

Convert the quadratic equation y = x^2 + 14x + 50 to vertex form.

Back

y = (x + 7)^2 + 1.

Front

What is the significance of the term (b/2)^2 in completing the square?

Back

The term (b/2)^2 is added to complete the square, ensuring the quadratic expression can be factored into a perfect square trinomial.

Front

How do you solve the equation a^2 + 10a + 21 = 0 by completing the square?

Back

First, subtract 21 from both sides to get a^2 + 10a = -21.

Front

What is the completed square form of the expression x^2 - 14x?

Back

x^2 - 14x can be written as (x - 7)^2 - 49.

Front

What are the roots of the equation 2x^2 - 20x + 18 = 0 after completing the square?

Back

The roots are x = {1, 9}.