Vertex-Form

Front

What is the vertex form of a quadratic function?

Back

The vertex form of a quadratic function is given by: 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.

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 axis of symmetry represent in a quadratic function?

Back

The axis of symmetry is a vertical line that passes through the vertex of the parabola, dividing it into two mirror-image halves.

Front

How can you find the axis of symmetry from the vertex form of a quadratic function?

Back

The axis of symmetry can be found using the formula x = h, where (h, k) is the vertex.

Front

What is the significance of the 'a' value in the vertex form of a quadratic function?

Back

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

Front

Convert the function f(x) = x² - 8x + 1 to vertex form.

Back

The vertex form is f(x) = (x - 4)² - 15.

Front

What is the vertex of the function f(x) = -2(x + 3)² + 5?

Back

The vertex of the function is (-3, 5).

Front

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

Back

The vertex can be identified directly as (h, k) from the vertex form f(x) = a(x - h)² + k.

Front

What is the effect of changing the 'k' value in the vertex form of a quadratic function?

Back

Changing the 'k' value shifts the graph vertically up or down without affecting the shape.