Graphing Functions and Analyzing Quadratics

The video tutorial covers converting quadratic functions to vertex form using Desmos, proving algebraic claims, understanding symmetry in graphs, analyzing a rocket's height and rate of change over time, and modeling prize distribution in a talent contest. It emphasizes practical applications of algebra and graphing techniques.

What is the standard form of the function discussed in the video?

• f(x) = 2x^2 + 6x - 8

• f(x) = x^2 + 3x - 4

• f(x) = 3x^2 + 2x - 5

• f(x) = 4x^2 + 5x - 6

Which tool is recommended for graphing the function?

• GraphCalc

• Wolfram Alpha

• Desmos

• GeoGebra

What is the vertex form of the function f(x) = 2x^2 + 6x - 8?

• 2(x + 1.5)^2 - 12.5

• 2(x - 1.5)^2 - 12.5

• 2(x + 3)^2 - 4

• 2(x - 3)^2 - 4

What is the correct answer choice for the vertex form of the function?

• Choice A

• Choice D

• Choice B

• Choice C

What is the claim about the points on the graph of f(x) = x(x-4)?

• If (2 + b, y) is on the graph, then (2 - d, y) is also on the graph.

• If (2 + d, y) is on the graph, then (2 - b, y) is also on the graph.

• If (2 + d, y) is on the graph, then (2 - d, y) is also on the graph.

• If (2 + b, y) is on the graph, then (2 - b, y) is also on the graph.

What method is used to verify the claim about the graph points?

• Graphical method

• Algebraic method

• Numerical method

• Statistical method

What is the line of symmetry for the graph of f(x) = x(x-4)?

• x = 2

• x = 1

• x = 3

• x = 0

Why is the line x = 2 significant for the graph of f(x)?

• It is the line of symmetry.

• It is the vertex.

• It is the x-intercept.

• It is the y-intercept.

What is the initial height of the rocket launched by Melissa?

• 3 meters

• 2 meters

• 1 meter

• 4 meters

What is the maximum height reached by the rocket?

• 50 meters

• 23 meters

• 34.25 meters

• 45 meters