Transformations & Quadratics in Vertex Form Practice

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 indicate?

Back

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

Front

What transformation is represented by a negative 'a' value in the vertex form?

Back

A negative 'a' value represents a reflection of the parabola across the x-axis.

Front

How does a vertical compression affect the graph of a quadratic function?

Back

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

Front

What transformation occurs when the 'h' value in the vertex form is positive?

Back

A positive 'h' value results in a horizontal translation of the graph to the right.

Front

What transformation occurs when the 'k' value in the vertex form is positive?

Back

A positive 'k' value results in a vertical translation of the graph upwards.

Front

How do you determine if a parabola is wider or narrower than the parent function y = x²?

Back

A parabola is wider than the parent function if |a| < 1 and narrower if |a| > 1.

Front

What is the effect of a horizontal translation on the graph of a quadratic function?

Back

A horizontal translation shifts the graph left or right without changing its shape.

Front

What does a vertical stretch by a factor of 'k' do to the graph of a quadratic function?

Back

A vertical stretch by a factor of 'k' (where k > 1) makes the parabola narrower.

Front

How do you represent a translation of 3 units to the left in the vertex form?

Back

To represent a translation of 3 units to the left, you would use f(x) = a(x + 3)² + k.