7A, 7C Quadratic Attributes and Transformations

Front

What is the vertex of the quadratic equation y = a(x-h)² + k?

Back

The vertex is the point (h, k).

Front

What does the value of 'a' in the quadratic equation y = a(x-h)² + k indicate about the graph?

Back

If 'a' is positive, the graph opens upwards; if 'a' is negative, the graph opens downwards.

Tags

CCSS.HSF-IF.C.7A

Front

How do you determine if a quadratic function has a maximum or minimum value?

Back

If 'a' is positive, the function has a minimum value; if 'a' is negative, it has a maximum value.

Front

What is the axis of symmetry for the quadratic equation y = a(x-h)² + k?

Back

The axis of symmetry is the vertical line x = h.

Front

How do you find the range of a quadratic function?

Back

The range depends on the vertex: if it opens upwards, the range is [k, ∞); if it opens downwards, the range is (-∞, k].

Front

What transformation does the equation y = a(x-h)² + k represent?

Back

It represents a vertical stretch/compression and a translation of the graph of y = ax² by h units horizontally and k units vertically.

Front

What does it mean for a quadratic function to be in vertex form?

Back

A quadratic function is in vertex form if it is expressed as y = a(x-h)² + k, where (h, k) is the vertex.

Front

How can you identify the direction in which a parabola opens from its equation?

Back

By examining the coefficient 'a': if 'a' > 0, it opens upwards; if 'a' < 0, it opens downwards.

Tags

CCSS.HSF-IF.C.7A

Front

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

Back

The vertex represents the maximum or minimum point of the graph, depending on the direction it opens.

Front

How do you convert a quadratic equation from standard form to vertex form?

Back

You can complete the square to rewrite the equation in the form y = a(x-h)² + k.