Algebra 1 9.4 f(x)=a(x-h)2+k

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

What does the parameter 'a' in the vertex form of a quadratic function represent?

Back

The parameter 'a' determines the direction and width of the parabola. If 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Front

How do you determine if a function is even?

Back

A function is even if f(-x) = f(x) for all x in the domain. This means the graph is symmetric about the y-axis.

Front

How do you determine if a function is odd?

Back

A function is odd if f(-x) = -f(x) for all x in the domain. This means the graph is symmetric about the origin.

Front

What does it mean if a function is neither even nor odd?

Back

A function is neither even nor odd if it does not satisfy the conditions for being even or odd, meaning it lacks symmetry about the y-axis or the origin.

Front

What is a translation in the context of graph transformations?

Back

A translation is a shift of the graph in the coordinate plane. For example, f(x) = (x-h)² + k translates the graph of f(x) = x² horizontally by h units and vertically by k units.

Front

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

Back

Changing 'h' in f(x) = a(x-h)² + k shifts the graph horizontally. If h is positive, the graph shifts to the right; if h is negative, it shifts to the left.

Front

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

Back

Changing 'k' in f(x) = a(x-h)² + k shifts the graph vertically. If k is positive, the graph shifts up; if k is negative, it shifts down.

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

How can you convert from standard form to vertex form?

Back

To convert from standard form to vertex form, you can complete the square.