Quadratic Transformations

Front

What is the parent function of a quadratic equation?

Back

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

Front

What transformation occurs when you add a number to the end of a quadratic function?

Back

A vertical shift occurs. If the number is positive, the graph shifts up; if negative, it shifts down.

Front

What does the equation y = (x - 3)² represent?

Back

A horizontal shift to the right by 3 units from the parent function y = x².

Front

What does the equation y = (x + 4)² represent?

Back

A horizontal shift to the left by 4 units from the parent function y = x².

Front

What transformation occurs when you subtract a number from the x variable in a quadratic function?

Back

A horizontal shift occurs. If the number is positive, the graph shifts left; if negative, it shifts right.

Front

What is the effect of a negative sign in front of a quadratic function, such as y = -x²?

Back

It reflects the graph across the x-axis.

Front

How do you identify a vertical shift in a quadratic function?

Back

Look for a constant added or subtracted from the function, such as in y = x² + k.

Front

What does the equation y = x² - 2 indicate about the graph's position?

Back

The graph is shifted down 2 units from the parent function y = x².

Front

What transformation is represented by the equation y = (x - 2)² + 3?

Back

A right shift of 2 units and an upward shift of 3 units from the parent function.

Front

What is the vertex of the function y = (x + 1)² - 4?

Back

The vertex is at the point (-1, -4).