Transforming Quadratic Functions

Front

What is the parent function of a quadratic equation?

Back

The parent function of a quadratic equation is y = x².

Front

How does the coefficient of x² affect the width of the parabola?

Back

If the coefficient is greater than 1, the parabola is narrower; if it is between 0 and 1, the parabola is wider.

Front

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

Back

This represents a vertical stretch/compression by a factor of |a|, a horizontal shift of h units, and a vertical shift of k units.

Front

What does a positive value of 'k' do in the function y = x² + k?

Back

A positive value of 'k' shifts the graph of the function upward.

Front

What does a negative value of 'h' do in the function y = (x + h)²?

Back

A negative value of 'h' shifts the graph of the function to the left.

Front

How do you shift the graph of f(x) = x² two units to the right?

Back

The equation becomes f(x) = (x - 2)².

Front

What is the effect of a negative coefficient in front of the quadratic function?

Back

A negative coefficient reflects the parabola across the x-axis.

Front

What transformation occurs in the function y = 3(x - 3)² + 3?

Back

The graph is shifted 3 units to the right and 3 units up, and it is narrower due to the coefficient 3.

Front

What does the term 'vertex' refer to in a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation.

Front

How do you identify the vertex of the function y = a(x - h)² + k?

Back

The vertex is at the point (h, k).