Transforming Quadratic Functions: Key Concepts and Techniques

This video tutorial covers transformations of quadratic functions, including horizontal and vertical shifts, reflections, and stretching. It explains the parent function y = x^2 and how to apply transformations to graph quadratic equations. The tutorial includes example problems to practice identifying and applying these transformations.

What is the y-value when x = -3 for the parent function y = x^2?

• -9

• 9

• 3

• 0

Which property of quadratic functions is highlighted by the fact that y-values are the same for x = -2 and x = 2?

• Periodicity

• Asymptote

• Symmetry

• Linearity

If a quadratic function is moved 4 units to the right, what is the new equation form?

• y = f(x) - 4

• y = f(x + 4)

• y = f(x - 4)

• y = f(x) + 4

What happens to the graph of y = x^2 when it is moved down 3 units?

• y = x^2 + 3

• y = x^2 - 3

• y = (x - 3)^2

• y = (x + 3)^2

In the equation y = (x + 4)^2 - 1, what transformations have been applied?

• Right 4, Down 1

• Left 4, Down 1

• Left 4, Up 1

• Right 4, Up 1

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

• The graph shifts left

• The graph shifts right

• The graph opens downward

• The graph opens upward

How does a vertical stretch by a factor of 2 affect the graph of y = x^2?

• The graph shifts up

• The graph becomes narrower

• The graph shifts down

• The graph becomes wider

For the function g(x) = -1/2 x^2, what transformations are applied?

• Reflection over y-axis and vertical shrink

• Reflection over x-axis and vertical stretch

• Reflection over x-axis and vertical shrink

• Reflection over y-axis and vertical stretch

In the equation h(x) = 2x^2 + 1, what is the effect of the +1?

• Shrinks the graph vertically

• Shifts the graph up 1 unit

• Stretches the graph vertically

• Shifts the graph down 1 unit

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

• (1, -2)

• (-1, 2)

• (-1, -2)

• (1, 2)