Algebra

[Candice]

What is the value of y at the x-intercept and why? What is the value of x at the y-intercept and why?

Is there any difference between solving a system of equation by the algebraic method as opposed to the graphical method? Explain.

 

[Deleted member 4993]

What is the value of y at the x-intercept and why? What is the value of x at the y-intercept and why?

What is the DEFINITION of x-intercept?

What is the DEFINITION of y-intercept?

Is there any difference between solving a system of equation by the algebraic method as opposed to the graphical method? Explain.

Solving an equation means - finding x-intercept/s (graphically)

Solving an equation means - finding the value/s of "x" at "y=0" (algebraic method)

 

[Mr.Pacman]

If you have a graphing calculator it is very easy to find both the X and Y intercepts

but first you need to understand what a x and y intercept is


X-intercepts

The x intercept (also called zeros of a function) will give you all the x values where Y is zero.
because When a function crosses over the x-axis at that point \(\displaystyle Y=0\) ,which is just like saying ,\(\displaystyle F(x) = 0\)

So in order to find the x-intercepts we must find where \(\displaystyle F(x) = 0\)
by setting all y values to zero...

Ex:

\(\displaystyle F(x)=x^2 + 6x\)

Steps to solve

\(\displaystyle 0 = x^2 + 6x\)

now we have to factor out a x

\(\displaystyle 0 = x(x+6)\)

now set them both equal to 0

\(\displaystyle x= 0\)
\(\displaystyle (x+6)= 0\)

then you will solve for x
so our x intercepts are at

\(\displaystyle x=0\)
\(\displaystyle x=-6\)


This is what you would see in a graphing calculator

You will do the same thing for the y-intercepts instead of changing "F(x)" to zero
you will change all the x's to zeros to find y-intercepts

 

[mathland]

What is the value of y at the x-intercept and why? ...At the x-intercept, the value of y = 0. This means that the graph of a given equation crosses the x-axis at some given point (b, 0).

What is the value of x at the y-intercept and why?...At the y-intercept, x = 0. This means the graph of a given equation crosses the y-axis at some given point (0, b).

Is there any difference between solving a system of equation by the algebraic method as opposed to the graphical method? Explain. ...Using the algebraic method allows us to find the solution to a systems of equations without having to make a picture of the equations on the xy-plane. By graphing, we can see where the equations cross, touch or meet each other on the xy-plane. Where they touch, meet or cross each other is the place of solution. By the way, we can also use matrix algebra to solve systems of equations.