Complete the Square

Front

What is the first step to solving the equation a² + 10a + 21 = 0 by completing the square?

Back

Subtract 21 from both sides.

Front

Solve the equation n² = 18n + 40 by completing the square.

Back

The solutions are {20, -2}.

Front

Solve the equation v² + 6v − 59 = 0 by completing the square.

Back

The solutions are {-3 + 2√17, -3 - 2√17}.

Front

What is one of the solutions to the equation (2x - 1)² = 49?

Back

One solution is -3.

Front

When factoring x² - 4x + 4 = 20, what goes in the blank? (x - __ )² = 20

Back

The blank is filled with 2.

Front

What does 'completing the square' mean in algebra?

Back

It is a method used to solve quadratic equations by rewriting them in the form (x - p)² = q.

Front

What is the standard form of a quadratic equation?

Back

The standard form is ax² + bx + c = 0.

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)).

Front

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

Back

The roots are the x-intercepts of the graph of the quadratic function.

Front

What is the formula for completing the square for the expression x² + bx?

Back

The formula is (x + b/2)² - (b/2)².