How to graph an equation

Graphs make it easier to analyze features of the equation like intercepts, increasing/decreasing, maxima/minima, concavity, etc. Examining a graph can reveal insights.

What are intercepts?

Intercepts refer to the points where a function or curve intersects the x-axis and y-axis. There are two main types of intercepts: x-intercepts and y-intercepts. Identifying these intercepts provides insight into the function and can help derive key characteristics.

What is an increasing/decreasing equation?

Increasing - The graph is rising as it moves left to right. The y-values increase as x increases.
Decreasing - The graph is falling as it moves left to right. The y-values decrease as x increases.

Identifying increasing/decreasing intervals helps understand the function's behavior.

What are maxima/minima?

Maxima and minima refer to the points where a function reaches its highest or lowest value.

Local maxima is the highest value in a region and global maxima when absolute highest over all x values.
Local minima is the lowest value in a region and global minima when absolute lowest over all x values.

What is concavity?

Concavity refers to the shape of the curve and whether it curves up or down.

The two types of concavity are:

Concave up - The curve resembles a cup or smile shape opening upwards. Indicates the rate of change is increasing.
Concave down - The curve resembles a frown shape curving downwards. Indicates the rate of change is decreasing.

Concavity

What are inflection points?

An inflection point is a point on the curve where the concavity changes from concave up to concave down or vice versa.

Graph an equation

Calculate values
Insert x y scatter chart
Change the x and y axis minimum and maximum value
Format x and y axis
Get Excel *.xlsx file

The picture above shows the following equation

x^3+3*x^2-3

plotted on an x y scatter chart.

1. Calculate values

Here are the instructions on how I built this chart:

Type -10 and -9 in cell A2:A3
Select cell A2:A3 and press and hold on the black dot.
Drag down until you see the number 10.
Release the mouse button
Select cell B2 and type: =A2^3+3*A2^2-3
Press Enter
Double press with left mouse button on dot in the lower right corner. This copies the formula to cells below as far as there are cells containing values in column A.

2. Insert x y scatter chart

Go to tab "Insert" on the ribbon
Press with mouse on scatter chart icon
Press with mouse on the scatter chart you prefer, I chose Scatter with straight lines.

3. Change the x and y axis minimum and maximum value

Press with right mouse button on on x axis
Press with mouse on "Format axis..."
Change minimum and maximum value
Change major units

Repeat with y axis.

4. Format x and y axis

Select x axis again
Press with mouse on Fill and Line icon
Select "Solid Line" and pick a color.
Repeat with y axis

How to comment

How to add a formula to your comment
<code>Insert your formula here.</code>

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