Completing the Square Practice

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax² + bx + c, where a, b, and c are constants.

Front

What is the vertex form of a quadratic equation?

Back

The vertex form of a quadratic equation is 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 - 14x?

Back

To complete the square, add (14/2)² = 49. The completed square is x² - 14x + 49.

Front

What is the missing number when completing the square for x² + 12x?

Back

The missing number is (12/2)² = 36. The completed square is x² + 12x + 36.

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is an expression of the form a² - 2ab + b², which factors to (a - b)².

Front

Identify the equivalent expression for the perfect square trinomial x² - 18x + 81.

Back

The equivalent expression is (x - 9)².

Front

What is the process of completing the square?

Back

Completing the square involves rewriting a quadratic in the form y = ax² + bx + c into the form y = a(x - h)² + k.

Front

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

Back

The vertex represents the highest or lowest point of the parabola, depending on the direction it opens.

Front

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

Back

The vertex (h, k) can be found using h = -b/(2a) and k = f(h).

Front

What does the 'a' value in a quadratic equation indicate?

Back

The 'a' value indicates the direction of the parabola: if a > 0, it opens upwards; if a < 0, it opens downwards.