Transformations of Quadratics

Front

What is the parent function of a quadratic?

Back

Front

What transformation shifts the graph of f(x) = x^2 to g(x) = (x + 4)^2?

Back

The transformation is a shift 4 units to the left.

Front

How do we transform from y = x^2 to y = -3x^2?

Back

The transformation involves a reflection in the x-axis and making the graph narrower.

Front

Does the graph of y = 5(x - 5)^2 + 3 widen or narrow from the parent function?

Back

The graph narrows compared to the parent function.

Front

If the blue graph is f(x) = x^2, what is the red graph if it is shifted 3 units to the right?

Back

The red graph is g(x) = (x - 3)^2.

Front

What effect does a negative coefficient have on the graph of a quadratic function?

Back

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

Front

What does it mean for a quadratic function to be 'narrower'?

Back

A quadratic function is narrower if the absolute value of the leading coefficient is greater than 1.

Front

What does it mean for a quadratic function to be 'wider'?

Back

A quadratic function is wider if the absolute value of the leading coefficient is less than 1.

Front

What is the vertex form of a quadratic function?

Back

Front

How does the value of 'h' in the vertex form affect the graph?

Back

The value of 'h' shifts the graph horizontally; if h is positive, the graph shifts to the right.