completing the square basic

Front

What is completing the square?

Back

Completing the square is a method used to solve quadratic equations by rewriting them in the form of a perfect square trinomial.

Front

What is the first step in completing the square for the equation a^2 + 10a + 21 = 0?

Back

Subtract 21 from both sides to isolate the quadratic expression.

Front

How do you find the value of c that makes x^2 - 12x + c a perfect square trinomial?

Back

Take half of the coefficient of x (which is -12), square it, and add it to c. The value of c should be 36.

Front

What is the formula for completing the square for a quadratic equation ax^2 + bx + c?

Back

The formula is: x = -b/(2a) ± √(b^2 - 4ac)/(2a). This helps to find the vertex of the parabola.

Front

What does it mean for a trinomial to be a perfect square?

Back

A trinomial is a perfect square if it can be expressed as (x + p)^2, where p is a real number.

Front

Solve the equation k^2 - 12k + 20 = 0 by completing the square.

Back

k = 10 and k = 2.

Front

What is the process to complete the square for the equation y^2 + 4y + 3 = 0?

Back

Subtract 3, take half of 4 (which is 2), square it to get 4, add 4 to both sides, and factor to get (y + 2)^2 = 1.

Front

What is the missing value in the equation x^2 + 6x + ____ to make it a perfect square?

Back

The missing value is 9.

Front

How do you convert the quadratic equation x^2 + bx + c into vertex form?

Back

By completing the square, you can rewrite it as (x - h)^2 + k, where (h, k) is the vertex.

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex represents the maximum or minimum point of the parabola, depending on the direction it opens.