H2 Maths Formulas, Techniques & Graphs >> Functions and Graphs >> Graphs >>
Solve equation by graphing in GC
Example
$$ x^4 - 2x = x^2 - 1 $$
There are two ways to solve the above equation.
Method 1: Graph the equation as 2 curves
1. In the GC, press 'y=' and plot $y_1 = x^4 - 2x$ and $y_2 = x^2 - 1$. Press 'graph' to obtain the graphs
2. Find the $x$-coordinates of the first point of intersection of the graphs:
- Press '2nd' - 'trace' and select '5: intersect'
- Select point on each curve that is close to the first point of intersection (Use < > keys to navigate and press 'enter' to select)
- Press 'enter' when prompted to 'guess'
3. Using the same method in Step 2, find the coordinates of the second point of intersection:
Method 2: Plot as a single function and find the x-intercepts
1. Bring all the terms to one side: \begin{align} x^4 - 2x & = x^2 - 1 \\ x^4 - x^2 - 2x + 1 & = 0 \end{align}
2. In the GC, press 'y=' and plot $y = x^4 - x^2 - 2x + 1$. Press 'graph' to obtain the graph
3. Find the first $x$-intercept of the graph:
- Press '2nd' - 'trace' and select '2: zero'
- Select the Left and Right bound such that the $x$-intercept is in the boundary (Use < > keys to navigate and press 'enter' to select)
- Press 'enter' when prompted to 'guess'
4. Using the same method in step 3, find the second x-intercept of the graph:
Finding large values of x by accessing table of values
$$ (0.05x - 8)^5 + 5 = 0 $$
To solve the equation above by graphing, plot $y = (0.05x - 8)^5 + 5$ and find the $x$-intercepts:
For cases like this, we need to use the table of values by pressing ‘2nd’ - ‘graph’:
Press ‘2nd’ - ‘window’ and change the increment (▵Tbl) to 20. Press ‘2nd’ - ‘graph’ to access the table:
Press ‘window’ and change
Xmin and Xmax to 120 and 140 respectively
(Optional) Ymin and Ymax to -40 and 40 respectively (to make sure y = 0 is included)
Press ‘graph’ and find the x-intercept (press ‘2nd’ - ‘trace’, select ‘2: zero’ and select the appropriate boundary):