Algebra 1 Practice - Graph an Absolute Value Equation on a Coordinate Plane (Example 2)
Please subscribe! / nickperich
To graph an absolute value equation in the form \( y = a|x - b| + c \), follow these steps:
1. *Understand the Components*
*Vertex:* The vertex of the graph is the point where the "V" shape begins. For the equation \( y = a|x - b| + c \), the vertex is \((b, c)\).
*Slope:* The coefficient \(a\) determines the steepness of the "V" shape and whether it opens upward or downward.
If \(a\) is positive, the graph opens upward.
If \(a\) is negative, the graph opens downward.
*Horizontal Shift:* The term \(b\) shifts the graph horizontally. The graph is shifted \(b\) units to the right if \(b\) is positive and to the left if \(b\) is negative.
*Vertical Shift:* The term \(c\) shifts the graph vertically. The graph is shifted \(c\) units up if \(c\) is positive and down if \(c\) is negative.
2. *Plot the Vertex*
Identify the vertex of the graph \((b, c)\) and plot this point on the coordinate plane.
3. *Determine the Direction of the "V" Shape*
Check the value of \(a\):
If \(a\) is positive, draw lines that slope upwards from the vertex.
If \(a\) is negative, draw lines that slope downwards from the vertex.
4. *Find Additional Points*
1. *Select a Point to the Left and Right of the Vertex:*
Choose a value for \(x\) on both sides of the vertex \(x = b\).
Substitute these values into the equation \( y = a|x - b| + c \) to find the corresponding \(y\)-values.
2. *Calculate and Plot These Points:*
For each selected \(x\), compute \( y \) and plot the resulting points.
5. *Draw the Graph*
Connect the plotted points with straight lines to form the "V" shape.
*Example:*
For the equation \( y = 2|x - 1| - 3 \):
1. *Vertex:*
The vertex is at \((1, -3)\). Plot this point.
2. *Direction:*
The coefficient \(2\) is positive, so the "V" opens upward.
3. *Find Additional Points:*
Choose \(x\) values to the left and right of \(x = 1\), for example \(x = 0\) and \(x = 2\):
For \(x = 0\):
\[
y = 2|0 - 1| - 3
\]
\[
y = 2 \cdot 1 - 3
\]
\[
y = 2 - 3 = -1
\]
Plot the point \((0, -1)\).
For \(x = 2\):
\[
y = 2|2 - 1| - 3
\]
\[
y = 2 \cdot 1 - 3
\]
\[
y = 2 - 3 = -1
\]
Plot the point \((2, -1)\).
4. *Draw the Graph:*
Connect the vertex \((1, -3)\) to \((0, -1)\) and \((2, -1)\) with straight lines to form the "V" shape.
This method will allow you to graph any absolute value equation of the form \( y = a|x - b| + c \).
I have many informative videos for Pre-Algebra, Algebra 1, Algebra 2, Geometry, Pre-Calculus, and Calculus. Please check it out:
/ nickperich
Nick Perich
Norristown Area High School
Norristown Area School District
Norristown, Pa
#math #algebra #algebra2 #maths #math #shorts #funny #help #onlineclasses #onlinelearning #online #study