Graphing a Quadratic Function

The video tutorial explains how to graph the quadratic function f(x) = -3x^2 + 8. It begins by selecting arbitrary X values, calculating corresponding f(x) values, and plotting these points on a graph. The tutorial demonstrates how to connect the points to form a downward-opening parabola, emphasizing the symmetry of the graph. The instructor encourages using graph paper for accuracy and explains the mathematical reasoning behind the curve's shape.

What is the general form of the function being graphed in the video?

• f(x) = -3x^2 - 8

• f(x) = 3x^2 - 8

• f(x) = -3x^2 + 8

• f(x) = 3x^2 + 8

Why are integers chosen for x-values in the video?

• They are more interesting.

• They are easier to calculate with.

• They are closer to zero.

• They are more accurate.

What is the value of f(x) when x = -2?

• -4

• 8

• -8

• 4

What point is plotted when x = 0?

• (0, -8)

• (0, 4)

• (0, 8)

• (0, 0)

What is the value of f(x) when x = 1?

• 5

• -5

• -8

• 8

What is the shape of the graph of the function?

• An upward opening parabola

• A straight line

• A circle

• A downward opening parabola

What is the value of f(x) when x = 2?

• -8

• 4

• -4

• 8

What is the symmetry property of the parabola discussed in the video?

• It has no symmetry.

• It is symmetric about the x-axis.

• It is symmetric about the y-axis.

• It is symmetric about the origin.

Why does f(x) have the same value for positive and negative x-values?

• Because the function is linear.

• Because the x-values are squared.

• Because the function is constant.

• Because the function is exponential.

What additional points are suggested to verify the shape of the parabola?

• Negative and positive fractions

• Negative and positive decimals

• Negative and positive whole numbers

• Negative and positive integers