3.5 Vertex Form/Completing the Square

Front

What is the vertex form of a quadratic function?

Back

The vertex form of a quadratic function is f(x) = 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 the expression: x² + bx + (b/2)².

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is an expression of the form a² ± 2ab + b², which can be factored as (a ± b)².

Front

How do you convert a quadratic equation to vertex form?

Back

To convert to vertex form, complete the square on the quadratic expression.

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.

Front

What is the process of factoring a perfect square trinomial?

Back

To factor a perfect square trinomial, identify the square root of the first and last terms and write it as (a ± b)².

Front

Given f(x) = x² + 8x + 16, what is its vertex form?

Back

f(x) = (x + 4)², since it is a perfect square trinomial.

Front

How do you find the value to complete the square for x² + 10x?

Back

Take half of 10 (which is 5), square it (25), and add it: x² + 10x + 25.

Front

What is the vertex of the function f(x) = 2(x - 3)² + 4?

Back

The vertex is (3, 4).

Front

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

Back

From the standard form f(x) = ax² + bx + c, the vertex can be found using h = -b/(2a) and k = f(h).