7.6: Extracting the Equation from a Graph
The graph of a cubic function starts at the point (2, 2). It passes through the point (10, 2). What is the equation of the function?
Guidance
This concept is the opposite of the previous two. Instead of graphing from the equation, we will now find the equation, given the graph.
Example A
Determine the equation of the graph below.
Solution:
From the previous two concepts, we know this is a square root function, so the general form is
4&=a \sqrt{4} \\
4&=2a \\
2&=a
The equation is
Example B
Find the equation of the cubed root function where
Solution:
First, plug in what we know to the general equation;
1&=3a \\
 \frac{1}{3}&=a
The equation of the function is
Example C
Find the equation of the function below.
Solution:
It looks like
2&=a \sqrt[3]{1} \\
2&=a
The equation of this function is
When finding the equation of a cubed root function, you may assume that one of the given points is
Intro Problem Revisit
First, plug in what we know to the general equation;
2&=a\sqrt[3]{8}+2\\
2&=2a +2\\
4&=2a\\
a = 2
The equation of the function is
Guided Practice
Find the equation of the functions below.
1.
2.
3. Find the equation of a square root equation with a starting point of
Answers
1. Substitute what you know into the general equation to solve for
7&=a \sqrt[3]{35}+8 \\
1&=2a \\
\frac{1}{2}&=a
The equation of this function is
2. Substitute what you know into the general equation to solve for
1&=a \sqrt{134}11 \\
12&=3a \\
4&=a
The equation of this function is
3. Substitute what you know into the general equation to solve for
6&=a \sqrt{4+5}3 \\
3&=3a \\
1&=a
The equation of this function is
Explore More
Write the equation for each function graphed below.

Write the equation of a square root function with starting point
(−6,−3) passing through(10,−15) . 
Write the equation of a cube root function with
(h,k)=(2,7) passing through(10,11) . 
Write the equation of a square root function with starting point
(−1,6) passing through(3,16) . 
Write the equation of a cubed root function with
(h,k)=(−1,6) passing through(7,16) . 
Write the equation of a cubed root function with
(h,k)=(7,16) passing through(−1,6) .  How do the two equations above differ? How are they the same?
Image Attributions
Description
Learning Objectives
Here you'll look at the graph of a square root or cubed root function and determine the equation.
Difficulty Level:
At GradeSubjects:
Concept Nodes:
Date Created:
Mar 12, 2013Last Modified:
Jun 04, 2015Vocabulary
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