Understanding Quadratic Functions and Parabolas

This video tutorial explains how to graph quadratic functions by creating a table of values and determining the vertex. It covers the properties of parabolas, including how the coefficients A, B, and C affect the graph's direction and width. The tutorial demonstrates how to calculate the vertex and plot points on the graph, emphasizing the importance of symmetry in parabolas.

What shape does the graph of a quadratic function form?

• A straight line

• A parabola

• An ellipse

• A circle

If the coefficient A in a quadratic function is negative, in which direction does the parabola open?

• Downward

• Upward

• To the left

• To the right

What happens to the width of a parabola if the absolute value of A is less than one?

• It becomes a straight line

• It remains the same

• It becomes wider

• It becomes narrower

Why is it beneficial to select x-values that are multiples of three when plotting points for the function f(x) = -1/3x^2 + 3x - 2?

• To find the vertex

• To avoid fractional y-values

• To make calculations easier

• To ensure symmetry

What is the y-coordinate of the vertex if the x-coordinate is 4.5 for the function f(x) = -1/3x^2 + 3x - 2?

• 4.75

• 3.5

• 5

• 4.5

What is the formula to find the x-coordinate of the vertex of a parabola?

• x = -B/2A

• x = -C/2A

• x = B/2A

• x = C/2A

Which point on the graph of a parabola is known as the vertical intercept?

• (0, y)

• (0, 0)

• (x, 0)

• (x, y)

What is the axis of symmetry in a parabola?

• A line parallel to the x-axis

• A vertical line through the vertex

• A diagonal line through the vertex

• A horizontal line through the vertex

How does the right side of a parabola relate to the left side?

• It is a mirror image

• It is identical

• It is perpendicular

• It is unrelated

What is the significance of the vertex in the graph of a parabola?

• It is the midpoint

• It is the highest or lowest point

• It is the starting point

• It is the end point