Understanding Quadratic Functions

This lecture explores quadratic functions, focusing on the general and vertex forms. It explains how the constants a, b, and c in the general form affect the shape and position of a parabola, while the vertex form provides a more intuitive understanding of the parabola's vertex coordinates. The lecture also demonstrates how to sketch a quadratic function's graph using the vertex form, highlighting the role of constants h and k in determining the vertex's position.

What is the general form of a quadratic function?

• ax^2 + bx

• ax + b

• ax^2 + bx + c

• ax^2 + c

Which constant affects the shape of the parabola in the general form?

• None of the above

• c

• a

• b

How does increasing the value of 'a' affect the parabola?

• It makes the parabola wider

• It shifts the parabola down

• It shifts the parabola up

• It makes the parabola narrower

What happens to the parabola when 'b' and 'c' are both zero?

• The parabola becomes a line

• The parabola opens down

• The vertex is at the origin

• The parabola shifts to the right

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

• The coordinates of the vertex

• The width of the parabola

• The slope of the parabola

• The direction the parabola opens

How does the vertex form make it easier to sketch a parabola?

• By providing the slope

• By simplifying the equation

• By showing the vertex coordinates

• By indicating the parabola's width

What is the vertex of the function one-third (x-3)^2 - 1?

• (3, -1)

• (-3, -1)

• (3, 1)

• (-3, 1)

If 'a' is positive in vertex form, which direction does the parabola open?

• Downwards

• Upwards

• To the left

• To the right

What additional information is needed to determine the horizontal stretch of a parabola?

• The value of 'b'

• The value of 'c'

• One additional point on the parabola

• The value of 'h'

Why is it not obvious why 'h' and 'k' are the vertex's coordinates?

• Because they are not part of the equation

• Because they are not constants

• Because they are not visible on the graph

• Because it requires further explanation