Understanding Quadratic and Linear Functions

This video tutorial covers graphing linear and quadratic equations. It begins with linear equations in slope-intercept form, explaining how to identify the slope and y-intercept, and how to plot them on a graph. The tutorial then moves to graphing equations in standard form by finding x and y-intercepts. It introduces quadratic functions, explaining transformations and how to graph them. The video concludes with advanced techniques for graphing quadratic functions, including factoring and finding the vertex and axis of symmetry.

What is the first step in graphing a linear equation in slope-intercept form?

• Plot the x-intercept

• Identify the slope

• Plot the y-intercept

• Draw a horizontal line

In the equation y = -3/4x + 5, what does the -3/4 represent?

• The y-intercept

• The slope

• The axis of symmetry

• The x-intercept

How do you find the x-intercept of a linear equation in standard form?

• Set y to zero and solve for x

• Find the midpoint of the line

• Set x to zero and solve for y

• Use the slope formula

What is the y-intercept of the equation 2x - 3y = 6?

• (0, -2)

• (3, 0)

• (0, 2)

• (-3, 0)

What is the effect of adding a constant to x^2 in a quadratic function?

• Shifts the graph horizontally

• Changes the slope of the graph

• Shifts the graph vertically

• Reflects the graph over the x-axis

How does the graph of y = (x - 2)^2 differ from y = x^2?

• It is shifted 2 units down

• It is shifted 2 units to the left

• It is shifted 2 units to the right

• It is shifted 2 units up

What is the axis of symmetry for the quadratic function y = x^2 - 6x + 8?

• x = 3

• x = 2

• x = 5

• x = 4

Which method can be used to find the x-intercepts of a quadratic function?

• Finding the vertex

• Graphing the function

• Using the zero product property

• Completing the square

What is the purpose of centering a data table around the vertex when graphing a quadratic function?

• To find the y-intercept

• To determine the axis of symmetry

• To ensure symmetry in the graph

• To calculate the slope

Where can you find additional resources for graphing different types of functions?

• In the video thumbnail

• In the video title

• In the video comments

• In the video description