Graphical Solutions of Polynomial Equations

The video tutorial explains how to solve the equation f(x) = x^3 + 6x - 2 = -10 graphically. It involves graphing f(x) and a constant function g(x) = -10, and finding their intersection point. The solution is identified as the x-value where the graphs intersect, which is x = 3. The tutorial concludes with entering the solution in the provided box.

What is the equation we are trying to solve graphically?

• x^3 + 6x - 2 = 10

• x^3 + 6x - 2 = 0

• x^3 + 6x - 2 = 6

• x^3 + 6x - 2 = -10

What does the function g(x) represent in this problem?

• An exponential function

• A quadratic function

• A constant function

• A linear function

How do we find the solution to the equation graphically?

• By finding the maximum point of f(x)

• By finding the intersection points of f(x) and g(x)

• By finding the y-intercepts of f(x)

• By finding the x-intercepts of f(x)

What is the shape of the graph of g(x) = -10?

• A parabola

• A horizontal line

• A cubic curve

• A vertical line

At what x-value do the graphs of f(x) and g(x) intersect?

• x = 2

• x = 0

• x = 1

• x = 3

What is the y-coordinate of the intersection point of f(x) and g(x)?

• 0

• -10

• -2

• 10

What ordered pair represents the intersection point of f(x) and g(x)?

• (3, 0)

• (3, -10)

• (0, -10)

• (0, 3)

What is the solution to the equation x^3 + 6x - 2 = -10?

• x = 3

• x = 2

• x = 1

• x = 0

How should multiple solutions be entered if they exist?

• Separated by a dash

• Separated by a space

• Separated by a comma

• Separated by a semicolon

How many solutions does the equation have?

• Three

• One

• Two

• None