Transformations 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 can you determine if a parabola opens upwards or downwards from its vertex form?

Back

If the coefficient 'a' in the vertex form f(x) = a(x - h)² + k is positive, the parabola opens upwards. If 'a' is negative, it opens downwards.

Front

What does it mean to stretch or compress a quadratic function vertically?

Back

A vertical stretch occurs when the absolute value of 'a' is greater than 1, making the parabola narrower. A vertical compression occurs when the absolute value of 'a' is less than 1, making the parabola wider.

Front

What transformations occur when the vertex form is written as f(x) = a(x - h)² + k?

Back

The transformations include a horizontal shift to the right by 'h' units, a vertical shift up by 'k' units, and a vertical stretch/compression/reflection based on the value of 'a'.

Front

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

Back

The vertex of the quadratic function in vertex form f(x) = a(x - h)² + k is the point (h, k).

Front

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

Back

A negative 'a' value reflects the parabola across the x-axis.

Front

How do you find the axis of symmetry for a quadratic function in vertex form?

Back

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

Front

What does it mean for a quadratic function to be reflected over the x-axis?

Back

Reflection over the x-axis means that the graph of the function is flipped upside down, which occurs when the leading coefficient 'a' is negative.

Front

How can you determine the direction of the opening of a parabola from its equation?

Back

By examining the sign of the coefficient 'a' in the vertex form f(x) = a(x - h)² + k; if 'a' is positive, it opens upwards, and if 'a' is negative, it opens downwards.

Front

What is the significance of the values 'h' and 'k' in the vertex form of a quadratic function?

Back

The values 'h' and 'k' represent the coordinates of the vertex of the parabola, which is the highest or lowest point of the graph depending on the direction it opens.