Quadratic transformations

Front

What is a quadratic transformation?

Back

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

Front

How does the equation y = x^2 transform to y = x^2 + 8?

Back

The graph is shifted up 8 units.

Front

What does it mean to stretch a graph vertically by a factor of 4?

Back

It means that for every point on the graph, the y-coordinate is multiplied by 4, making the graph taller.

Front

What is the effect of reflecting a graph over the x-axis?

Back

It flips the graph upside down, changing the sign of all y-coordinates.

Front

How do you transform y = x^2 to y = 2(x + 2)^2 - 5?

Back

You stretch the graph vertically by a factor of 2, shift it 2 units left, and 5 units down.

Front

What is the parent function of a quadratic equation?

Back

The parent function of a quadratic equation is y = x^2.

Front

What does a vertical shift of a quadratic function do?

Back

A vertical shift moves the graph up or down without changing its shape.

Front

How does the equation y = -3(x - 1)^2 + 2 transform the graph of y = x^2?

Back

It reflects the graph over the x-axis, stretches it vertically by a factor of 3, shifts it 1 unit right, and 2 units up.

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex is the highest or lowest point of the graph, depending on the direction it opens.

Front

How do horizontal shifts affect the graph of a quadratic function?

Back

Horizontal shifts move the graph left or right, changing the x-coordinates of the vertex.