Graphing Quadratics in Vertex Form

This video tutorial covers graphing quadratic equations in vertex form by understanding transformations from the parent function. It explains the role of each parameter in the vertex form equation and how they affect the graph's position and shape. The tutorial includes examples of graphing quadratics with different transformations, such as vertical stretches, compressions, and reflections. It also guides on describing transformations and writing equations based on given transformations.

What is the parent function of a quadratic equation?

• y = x^3

• y = x^2

• y = x + 2

• y = 2x

What does the parameter 'k' in the vertex form of a quadratic equation affect?

• Horizontal shifts

• Vertical shifts

• Reflection over the x-axis

• Stretching the graph vertically

If a quadratic graph is reflected over the x-axis, what is the sign of 'a'?

• Undefined

• Zero

• Negative

• Positive

How does a negative 'h' value affect the graph of a quadratic equation in vertex form?

• Moves it right

• Moves it down

• Moves it up

• Moves it left

What happens to the graph of a quadratic when the absolute value of 'a' is greater than 1?

• It becomes wider

• It shifts to the right

• It becomes narrower

• It shifts to the left

What is the vertex of the quadratic equation y = (x - 3)^2 + 4?

• (3, -4)

• (-3, 4)

• (3, 4)

• (-3, -4)

If the quadratic equation is y = 2(x + 2)^2 - 3, where is the vertex located?

• (2, 3)

• (2, -3)

• (-2, -3)

• (-2, 3)

What transformation is described by a vertical stretch by a factor of 3?

• y = (x/3)^2

• y = (x - 3)^2

• y = 3(x - 1)^2

• y = x^2 + 3

How would you describe the transformation for the equation y = -1/2(x + 4)^2 + 5?

• Reflected over the y-axis, vertically compressed by a factor of 2, translated left 4 units and down 5 units

• Reflected over the y-axis, vertically stretched by a factor of 2, translated right 4 units and up 5 units

• Reflected over the x-axis, vertically compressed by a factor of 2, translated left 4 units and up 5 units

• Reflected over the x-axis, vertically compressed by a factor of 2, translated right 4 units and up 5 units

Which equation represents a parabola that has been translated 3 units down and 2 units to the right?

• y = (x + 2)^2 + 3

• y = (x - 2)^2 + 3

• y = (x - 2)^2 - 3

• y = (x + 2)^2 - 3