Quadratic Function - 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 find the axis of symmetry for a parabola in vertex form?

Back

The axis of symmetry for a parabola in vertex form f(x) = a(x - h)² + k is the vertical line x = h.

Front

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

Back

The 'a' value indicates the direction of the parabola (upward if a > 0, downward if a < 0) and the width (narrower if |a| > 1, wider if |a| < 1).

Front

If a parabola opens upwards, what can be said about its vertex?

Back

If a parabola opens upwards, the vertex represents the minimum point of the function.

Front

If a parabola opens downwards, what can be said about its vertex?

Back

If a parabola opens downwards, the vertex represents the maximum point of the function.

Front

How do you determine the vertex from the equation y = 2(x + 3)² + 4?

Back

The vertex is (-3, 4) because it is in the form y = a(x - h)² + k, where h = -3 and k = 4.

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex is the highest or lowest point on the graph of the quadratic function, depending on whether it opens upwards or downwards.

Front

What is the formula to convert standard form to vertex form?

Back

To convert from standard form ax² + bx + c to vertex form, use the method of completing the square.

Front

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

Back

Changing the 'k' value in the vertex form f(x) = a(x - h)² + k shifts the graph vertically up or down.

Front

What is the effect of changing the 'h' value in the vertex form?

Back

Changing the 'h' value in the vertex form f(x) = a(x - h)² + k shifts the graph horizontally left or right.