Standard Form to Vertex Form

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax² + bx + c, where a, b, and c are constants.

Front

What is 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 from standard form to vertex form?

Back

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

Front

What is the vertex of the function f(x) = (x - 4)² - 15?

Back

The vertex of the function is (4, -15).

Front

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

Back

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

Front

What is the axis of symmetry for the function f(x) = x² - 8x + 1?

Back

The axis of symmetry is x = 4, which is found using the formula x = -b/(2a).

Front

Convert f(x) = 4x² - 32x + 2 to vertex form.

Back

f(x) = 4(x - 4)² - 62.

Front

Convert y = x² + 8x + 20 to vertex form.

Back

y = (x + 4)² + 4.

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 y = x² - 6x + 13 to vertex form.

Back

y = (x - 3)² + 4.