Quadratic Functions and Graphing

This video tutorial reviews quadratic functions, focusing on graphing them in general form. It explains the properties of quadratic functions, such as the parabola shape, line of symmetry, and vertex. The video demonstrates how to use sliders to adjust coefficients and observe changes in the graph. It provides examples of graphing quadratic functions, including using a graphing calculator for more complex cases. The tutorial emphasizes understanding the axis of symmetry and vertex to accurately graph quadratic functions.

What shape does the graph of a quadratic function typically take?

• A triangle

• A straight line

• A circle

• A parabola

When does a parabola open upwards?

• When 'A' is equal to zero

• When 'A' is less than zero

• When 'A' is greater than zero

• When 'B' is greater than zero

What is the line of symmetry for a quadratic function?

• X = B/2A

• Y = -B/2A

• X = -B/2A

• Y = B/2A

How do you find the vertex of a parabola?

• By using the line of symmetry and substituting into the function

• By finding the midpoint of the intercepts

• By finding the average of the coefficients

• By setting the derivative to zero

What happens to the parabola when the value of 'A' increases?

• It becomes wider

• It shifts to the right

• It becomes narrower

• It shifts to the left

What effect does changing the value of 'C' have on the graph?

• It causes a vertical shift

• It changes the direction of the parabola

• It changes the width of the parabola

• It causes a horizontal shift

In the example F(x) = x^2 - 4x - 5, what is the x-coordinate of the vertex?

• 4

• 3

• 2

• 1

What are the x-intercepts of the function F(x) = x^2 - 4x - 5?

• (2, 0) and (-2, 0)

• (3, 0) and (1, 0)

• (4, 0) and (0, 0)

• (5, 0) and (-1, 0)

Why does the parabola in the second example open downward?

• Because 'C' is negative

• Because 'A' is positive

• Because 'B' is positive

• Because 'A' is negative

What is the significance of the axis of symmetry in graphing a parabola?

• It determines the width of the parabola

• It helps in finding mirror image points

• It indicates the maximum value

• It shows the minimum value