#### Theory of Solving Equations Graphically

Solving Equations Graphically:

Intercepts:

x-intercept: The x-intercept is a point where the graph of an equation crosses x-axis. The x-intercept can be found by replacing y = 0 to the equation and solving for x. The x-intercept is also termed as a solution, root, or the zero of equation.

y-intercept: The y-intercept is a point where the graph of an equation crosses y-axis. The y-intercept can be found by replacing x = 0 to the equation and solving for y.

There is no need that an equation has either an x-intercept or y-intercept. It is too possible that there might be more than one of each and every intercept.

Intercept, Root, Zero, Solution:

The given below statements are equivalent to:

a) The point (a, 0) is an x-intercept of graph of y = f(x)
b) x = a is zero or root of the function f.
c) x = a is the solution of equation f(x) = 0
d) (x - a) is a factor of f(x)

Finding roots with the Graphing Calculator:

To determine the roots of a function by using the graphing calculator, it might be essential to put the equation to standard form f(x) = 0. To accomplish this, you might require moving everything over to one side of equation. It doesn’t matter that side you move the terms to, the solutions will be similar either way. Then, graph the equation y = f(x) on the calculator.

There is a much simpler and more precise way to use the zoom and trace features of your calculator to find the zeros of a function.

a) Use [Calc] (2nd Trace) key and select the zero (TI83) and root (TI82) option.

b) Whenever it asks for the left or lower bound, then use the left arrow key to place the cursor to the left of zero and hit the [Enter] key.

c) Whenever it asks for the right or upper bound, then use the right arrow key to place the cursor to the right of zero and hit the [Enter] key.

d) Whenever it asks for a guess and then use the left arrow key to move back to the point nearest to the x-intercept and hit the [Enter] key.

e) The x-coordinate returned the x-intercept, root, zero, or solution which you're looking for.
The trace and zoom method will work, however it is a whole lot faster and more precise, to use the options beneath [Calc].

Finding Intersections with the Graphing Calculator:

To determine the intersection of two equations with graphing calculator, enter the two functions to the calculator as y1 and y2 and graph them both. Play around with viewing window till you determine the point of intersection and then....

a) Utilize the [Calc] key and select the intersect option.

b) This will ask for the first curve. When there are just two plots active, then you can simply hit [Enter] as it defaults to the first curve. When you have more than two plots active, then utilize the up or down arrow keys to choose the proper function, and then hit enter. It doesn’t matter where on the curve you hit enter.

c) This will ask for the second curve. When there are just two plots active, then you can just press [Enter]. Use up or down arrow keys when you need to choose a different function.

d) It then requests for a guess. Use left or right arrow keys to move to a place near to the point of intersection and hit [Enter].

e) The x-coordinate and y-coordinate of the point of intersection are come back.

This is possible to find out the solution to an equation in non-standard form by supposing the y1 plot be left hand side of the equation, the y2 plot being the right hand side of equation, and utilizing the intersect option. Though, it is much more convenient and time effective to rewrite the equation in standard form and utilize the zero or root option rather.

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