Transformations of Quadratic Functions

Front

What is a transformation of a quadratic function?

Back

A transformation of a quadratic function refers to changes made to the graph of the function, such as shifts, reflections, and stretches or compressions.

Front

What does it mean for a graph to be reflected?

Back

A reflection of a graph occurs when it is flipped over a line, such as the x-axis, resulting in a mirror image.

Front

How does the coefficient of a quadratic function affect its width?

Back

If the coefficient (a) is greater than 1, the graph is narrower; if it is between 0 and 1, the graph is wider.

Front

What is the vertex form of a quadratic function?

Back

The vertex form of a quadratic function is given by y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

What does shifting a graph down 3 units mean?

Back

Shifting a graph down 3 units means subtracting 3 from the function, resulting in a new function of the form y = f(x) - 3.

Front

What is the parent function of a quadratic equation?

Back

The parent function of a quadratic equation is f(x) = x², which is the simplest form of a quadratic function.

Front

How does the graph of y = x² - 7 compare to y = x²?

Back

The graph of y = x² - 7 is shifted down 7 units from the parent function y = x².

Front

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

Back

A quadratic function is wider when its coefficient (a) is between 0 and 1, causing the parabola to open more gently.

Front

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

Back

A negative coefficient reflects the graph over the x-axis, making it open downwards.

Front

How can you identify the vertex of a quadratic function in vertex form?

Back

In vertex form y = a(x - h)² + k, the vertex is the point (h, k).