Understanding Quadratic Functions

What are the two common forms of a quadratic function?

• Standard form and linear form

• General form and vertex form

• General form and linear form

• Vertex form and linear form

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

• The color of the graph

• The width and direction of the parabola

• The height of the vertex

• The number of roots

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

• b over 2a

• Negative a over 2b

• Negative b over 2a

• a over 2b

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

• The slope and y-intercept

• The width and height of the parabola

• The roots of the equation

• The horizontal and vertical coordinates of the vertex

What happens to the graph of a quadratic function when you add a constant k in vertex form?

• It changes color

• It rotates

• It shifts vertically

• It shifts horizontally

How do you shift a quadratic function horizontally by h units?

• Add h to x

• Subtract h from x

• Multiply x by h

• Divide x by h

What is the effect of subtracting a positive value h from x in a quadratic function?

• The graph shifts h units to the left

• The graph shifts h units to the right

• The graph shifts h units up

• The graph shifts h units down

What is the process called that can also derive the vertex form from the general form?

• Integration

• Factoring

• Completing the square

• Differentiation

Can quadratic functions be converted between general form and vertex form?

• Yes, but only in special cases

• No, only vertex form can be converted to general form

• No, they are fixed forms

• Yes, they can be converted both ways

What will be covered in the next lecture?

• The history of quadratic functions

• Graphing techniques

• Formulas to convert between forms

• Applications of quadratic functions