Understanding Quadratic Functions

The video tutorial explains how to analyze and graph a quadratic function. It covers finding the axis of symmetry, vertex, X and Y intercepts, and graphing the function. The tutorial uses a specific quadratic function, F(x) = 2x^2 - 18, to demonstrate these concepts. The instructor reviews the properties of quadratic functions, including the parabola shape and the axis of symmetry formula. The video also includes a practical example of graphing the function using key points and verifying the graph with a software tool.

What is the first step in analyzing a quadratic function?

• Finding the y-intercept

• Graphing the function

• Identifying the axis of symmetry

• Calculating the vertex

Which of the following is true about the axis of symmetry in a quadratic function?

• It is always at y = 0

• It is a horizontal line

• It is given by the formula x = -b/2a

• It passes through the y-intercept

How do you find the x-coordinate of the vertex in a quadratic function?

• By setting y = 0

• Using the formula x = -b/2a

• By finding the y-intercept

• By solving the quadratic equation

What is the process to find the x-intercepts of a quadratic function?

• Setting y = 0 and solving for x

• Using the quadratic formula

• Finding the vertex

• Setting x = 0 and solving for y

When factoring the quadratic equation 0 = 2x^2 - 18, what is the first step?

• Factor out the greatest common factor

• Add 18 to both sides

• Divide by 2

• Use the quadratic formula

What are the x-intercepts of the function f(x) = 2x^2 - 18?

• x = 0 and x = 3

• x = -9 and x = 9

• x = -3 and x = 3

• x = 0 and x = 9

How is the y-intercept of a quadratic function determined?

• By using the formula y = -b/2a

• By setting x = 0 and solving for y

• By finding the vertex

• By setting y = 0 and solving for x

In the function f(x) = 2x^2 - 18, what is the y-intercept?

• (0, -18)

• (0, 18)

• (18, 0)

• (-18, 0)

Which point is both the vertex and the y-intercept in the function f(x) = 2x^2 - 18?

• (3, 0)

• (0, 18)

• (0, -18)

• (-3, 0)

What is the shape of the graph of a quadratic function?

• A parabola

• A circle

• A straight line

• An ellipse