Understanding Linear and Quadratic Equations

This video tutorial introduces linear equations and their standard form, AX + BY = C, where A, B, and C are real numbers. It explains how to identify linear equations and differentiate them from non-linear ones. The video focuses on finding x and y-intercepts of equations, demonstrating the process with examples. It covers graphing linear equations using intercepts and also touches on graphing non-linear equations, highlighting the differences. The tutorial aims to help viewers understand intercepts and graph equations effectively.

Which of the following is a characteristic of a linear equation in standard form?

• It includes an x squared term.

• It includes a product of variables.

• It has variables in the denominator.

• It is of the form AX + BY = C.

What makes an equation non-linear?

• Having a constant term.

• Having a variable in the denominator.

• Having a linear term.

• Having a zero constant.

Where does the y-intercept of a graph occur?

• Where the graph is horizontal.

• Where the graph is vertical.

• Where the graph crosses the y-axis.

• Where the graph crosses the x-axis.

How do you find the x-intercept of an equation's graph?

• Set x to 1 and solve for y.

• Set y to 1 and solve for x.

• Set x to 0 and solve for y.

• Set y to 0 and solve for x.

What is the x-intercept of the equation 3x - 2y = 12?

• (2, 0)

• (4, 0)

• (0, 4)

• (0, -6)

What is the y-intercept of the equation y = -2x + 4?

• (4, 0)

• (2, 0)

• (0, 4)

• (0, -2)

Which of the following is true about the graph of y = x^2 - 4?

• It has only one x-intercept.

• It is a parabola.

• It has no intercepts.

• It is a straight line.

How many x-intercepts does the equation y = x^2 - 4 have?

• Two

• None

• Three

• One

What is the y-intercept of the equation y = x^2 - 4?

• (4, 0)

• (0, -4)

• (2, 0)

• (0, 4)

Which shape does the graph of a quadratic equation typically form?

• Circle

• Ellipse

• Line

• Parabola