Exploring Transformations of Quadratic Functions

What is a necessary component for a function to be considered quadratic?

• It must have an x^3 term.

• It must have an x^2 term.

• It must have a constant term.

• It must have an x term.

Which of the following is NOT a quadratic function?

• y = 2x^2 + 3x + 1

• y = x^3 + 2x^2 + 1

• y = -x^2 + 4x - 5

• y = 0.5x^2 - x + 2

What shape does the graph of a quadratic function take?

• A parabola

• A hyperbola

• A straight line

• A circle

Which of the following describes a downward-facing parabola?

• It is a linear function.

• It is a cubic function.

• It is a positive function.

• It is a negative function.

In the vertex form y = a(x - h)^2 + k, what does the 'a' value determine?

• The direction and width of the parabola

• The vertical shift

• The horizontal shift

• The y-intercept

If 'a' is positive in the vertex form, how does the parabola open?

• To the left

• Downward

• Upward

• To the right

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

• It makes the parabola open downward.

• It makes the parabola open upward.

• It shifts the graph to the right.

• It shifts the graph to the left.

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

• It changes the direction of the graph.

• It changes the width of the graph.

• It moves the graph left or right.

• It moves the graph up or down.

What transformation occurs if 'k' is positive in the vertex form?

• The graph shifts upward.

• The graph shifts to the right.

• The graph shifts to the left.

• The graph shifts downward.

Given the equation y = 3(x + 2)^2 - 4, what is the transformation if we translate it up 2 units and left 5 units?

• y = 3(x + 7)^2 - 6

• y = 3(x - 3)^2 - 6

• y = 3(x - 3)^2 - 2

• y = 3(x + 7)^2 - 2