Solving Equations by Completing the Square

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 complete the square for the expression x² + bx?

Back

To complete the square, take half of b, square it, and add it to both sides of the equation. The expression becomes (x + b/2)² - (b/2)².

Front

What is the process of completing the square?

Back

Completing the square involves rewriting a quadratic equation in the form of a perfect square trinomial, allowing for easier solving and graphing.

Front

Convert the equation x² + 6x - 5 to vertex form.

Back

y = (x + 3)² - 14.

Front

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

Back

The vertex represents the maximum or minimum point of the parabola, indicating the highest or lowest value of the function.

Front

How do you find the vertex of a quadratic equation in standard form?

Back

For a quadratic in standard form y = ax² + bx + c, the vertex can be found using the formula h = -b/(2a) and k = f(h).

Front

Solve the equation n² - 2n - 3 = 0 by completing the square.

Back

The solutions are n = 3 and n = -1.

Front

What is the value to add to complete the square for x² + 12x?

Back

The value to add is 36, making the expression (x + 6)².

Front

What does it mean to convert to vertex form?

Back

Converting to vertex form means rewriting the quadratic equation to highlight its vertex, making it easier to analyze its properties.

Front

What is the first step in completing the square for x² + 6x?

Back

The first step is to take half of 6, which is 3, and square it to get 9.