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 convert a quadratic function to vertex form?

Back

To convert a quadratic function to vertex form, you can complete the square on the quadratic expression.

Front

What is completing the square?

Back

Completing the square is a method used to convert a quadratic equation into a perfect square trinomial, making it easier to analyze and graph.

Front

Given f(x) = ax² + bx + c, how do you find the vertex?

Back

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

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

Convert f(x) = 2x² + 8x + 10 to vertex form.

Back

f(x) = 2(x + 2)² + 6.

Front

Complete the square for x² + 6x + ____.

Back

The blank should be filled with 9, making it x² + 6x + 9 = (x + 3)².

Front

What is the axis of symmetry for a quadratic function?

Back

The axis of symmetry is the vertical line x = h, where (h, k) is the vertex of the parabola.

Front

How do you determine if a quadratic opens upwards or downwards?

Back

If the coefficient 'a' in f(x) = ax² + bx + c is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Front

Convert f(x) = 3x² - 12x + 5 to vertex form.

Back

f(x) = 3(x - 2)² - 7.