Graphing Quadratic Functions in Vertex Form

The video tutorial covers graphing quadratic functions, focusing on vertex form. It begins with the parent function y = x^2, explaining how to graph it and identify the vertex. The tutorial then explores transformations, including vertical and horizontal shifts, reflections, and the effects of coefficients on the parabola's width and direction. The concept of vertex form is introduced, detailing how each component affects the graph. Examples are provided to illustrate these concepts, including finding the zeros of a parabola.

What is the shape of the graph of a quadratic function?

• Hyperbola

• Parabola

• Ellipse

• Circle

Where is the vertex of the parent function y = x^2 located?

• (2, 2)

• (-1, -1)

• (1, 1)

• (0, 0)

What happens to the graph of y = x^2 when you add 3 to the function (y = x^2 + 3)?

• Shifts left 3 units

• Shifts up 3 units

• Shifts down 3 units

• Shifts right 3 units

What is the new vertex when you graph y = x^2 - 3?

• (0, 3)

• (0, -3)

• (3, 0)

• (-3, 0)

How does adding 3 inside the parentheses (y = (x + 3)^2) affect the graph?

• Shifts down 3 units

• Shifts right 3 units

• Shifts up 3 units

• Shifts left 3 units

What happens to the graph of y = (x - 3)^2?

• Shifts right 3 units

• Shifts down 3 units

• Shifts up 3 units

• Shifts left 3 units

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

• Shifts down

• Shifts up

• Reflects over the x-axis

• Reflects over the y-axis

How does a coefficient greater than 1 affect the graph of a quadratic function?

• Makes the graph narrower

• Makes the graph wider

• Shifts the graph left

• Shifts the graph right

In vertex form, what does the constant outside the parentheses indicate?

• Reflection

• Width change

• Vertical shift

• Horizontal shift

If the vertex form of a quadratic function is y = 2(x + 4)^2 - 5, where is the vertex located?

• (4, 5)

• (-4, -5)

• (4, -5)

• (-4, 5)