Solving Equations and Graphing Cubic Functions using Substitution Method

The video tutorial explains how to solve a cubic equation using the substitution method, plot the results on a graph, and find solutions by drawing a straight line to identify intersections. It covers the calculation of Y values, plotting coordinates, and interpreting the graph to find solutions.

What is the first step in using the substitution method to find Y values for a given X in a cubic equation?

• Plot the graph of the equation.

• Substitute the X value into the equation.

• Use a calculator to find the Y value.

• Estimate the Y value based on previous results.

When plotting a cubic graph, why is it important to be aware of the scale on the axes?

• To avoid using a calculator.

• To make the graph look symmetrical.

• To accurately plot the points and interpret the graph.

• To ensure the graph is colorful.

Why is it important not to use a ruler when joining points on the cubic graph?

• It is against the rules.

• It makes the graph too straight.

• It prevents the curve from being smooth.

• It makes the graph look messy.

What is the purpose of drawing a straight line on the graph in this context?

• To make the graph look more complex.

• To find the Y-intercept of the cubic equation.

• To estimate solutions for a modified equation.

• To check the accuracy of the cubic curve.

What is the difference between the original equation and the modified equation used in Part C?

• The coefficients of X^3 are different.

• The equations have different variables.

• The equations are identical.

• The constant term is different.

How do you determine the X values at the points of intersection between the cubic curve and the straight line?

• By measuring the distance between the points.

• By drawing vertical lines from the intersection points to the X-axis.

• By calculating the slope of the line.

• By using a ruler to connect the points.

What is the gradient of the straight line used to find solutions in Part C?

• -3

• 0

• 2

• -2

How many solutions are typically found at the intersection of the cubic curve and the straight line?

• Two

• Four

• One

• Three

What is the first mark awarded for in Part C of the task?

• Identifying all intersection points.

• Correctly plotting the cubic curve.

• Finding the difference between the equations.

• Using a ruler to draw the line.

What is the final mark in Part C awarded for?

• Having all three solutions correct.

• Using a calculator for accuracy.

• Drawing a colorful graph.

• Using a ruler to draw the line.