Convert from Standard to Vertex Form

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 convert a quadratic function from standard form to vertex form?

Back

To convert from standard form f(x) = ax² + bx + c 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 highest or lowest point of the parabola, depending on the direction it opens.

Front

What does the 'a' value in the vertex form indicate?

Back

The 'a' value determines the direction of the parabola (upward if a > 0, downward if a < 0) and its width.

Front

What is completing the square?

Back

Completing the square is a method used to convert a quadratic expression into a perfect square trinomial.

Front

Convert f(x) = 2x² + 8x + 3 to vertex form.

Back

f(x) = 2(x + 2)² - 5.

Front

Convert f(x) = x² - 6x + 9 to vertex form.

Back

f(x) = (x - 3)².

Front

What is the vertex of the function f(x) = 3(x - 1)² + 4?

Back

The vertex is (1, 4).

Front

How do you find the x-coordinate of the vertex from standard form?

Back

The x-coordinate of the vertex can be found using the formula x = -b/(2a) from the standard form f(x) = ax² + bx + c.

Front

Convert f(x) = -x² + 4x - 1 to vertex form.

Back

f(x) = -(x - 2)² + 3.