Algebra 67 - Deriving the Vertex Form of a Quadratic Function

The video tutorial by Professor Von Schmohawk at Why U explains the two common forms of quadratic functions: general form and vertex form. It discusses how the graph of a quadratic function is always a parabola and how the constants in each form affect the graph's shape and position. The tutorial covers calculating the vertex in general form and understanding the vertex form's h and k constants. It also explains how to shift graphs vertically and horizontally and introduces the concept of converting between general and vertex forms.

What are the two common forms of a quadratic function?

• Exponential and Logarithmic

• Polynomial and Rational

• General and Vertex

• Linear and Quadratic

In the general form of a quadratic function, what does the constant 'a' determine?

• The y-intercepts

• The color of the graph

• The width and direction of the parabola

• The x-intercepts

How can the x-coordinate of the vertex be calculated in the general form?

• By using the quadratic formula

• By setting y to zero

• By finding the midpoint of the x-intercepts

• Using the formula -b/2a

In vertex form, what do the constants h and k represent?

• The slope and y-intercept

• The horizontal and vertical coordinates of the vertex

• The roots of the equation

• The maximum and minimum values

What happens to a graph when a constant is added to a function?

• It becomes a straight line

• It rotates around the origin

• It shifts vertically

• It changes color

How is a parabola shifted horizontally in vertex form?

• By multiplying the function by a constant

• By replacing x with x minus h

• By adding a constant to the function

• By setting the derivative to zero

What is one method to derive the vertex form from the general form?

• Completing the square

• Finding the derivative

• Using synthetic division

• Using the quadratic formula