SOLUTION: hi i am having trouble working out how to do these graphs. could someone show me how to work it out and if they could do the graphs that would be much appreciated x Question:

Algebra ->  Graphs -> SOLUTION: hi i am having trouble working out how to do these graphs. could someone show me how to work it out and if they could do the graphs that would be much appreciated x Question:       Log On


   

Question 78255: hi i am having trouble working out how to do these graphs.
could someone show me how to work it out and if they could do the graphs that would be much appreciated x
Question:
plot a graph of the following curves and write down their co-ordinates of their intersection with the x- axis:
a, y=x²-x-2
b, y=2x²-3x-9
plot the graphs between x=-2 and x=+3
thanks for your help x
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
In order to graph y=x%5E2-x-2 lets make a table:

      x      y
   -5.0   28.0
   -4.0   18.0
   -3.0   10.0
   -2.0    4.0
   -1.0    0.0
    0.0   -2.0
    1.0   -2.0
    2.0    0.0
    3.0    4.0
    4.0   10.0
    5.0   18.0

Now draw a parabola through these points
+graph%28+300%2C+200%2C+-6%2C+5%2C+-10%2C+10%2C+x%5E2-x-2%29
In order to graph y=2x%5E2-3x-9 lets make a table:

     x      y
   -5.0   56.0
   -4.0   35.0
   -3.0   18.0
   -2.0    5.0
   -1.0   -4.0
    0.0   -9.0
    1.0  -10.0
    2.0   -7.0
    3.0    0.0
    4.0   11.0
    5.0   26.0

Now draw a parabola through these points
+graph%28+300%2C+200%2C+-6%2C+5%2C+-10%2C+10%2C+2x%5E2-3x-9%29+
So now use the quadratic formula for each case to find the x-intercepts
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-1x%2B-2+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-1%29%5E2-4%2A1%2A-2=9.

Discriminant d=9 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--1%2B-sqrt%28+9+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-1%29%2Bsqrt%28+9+%29%29%2F2%5C1+=+2
x%5B2%5D+=+%28-%28-1%29-sqrt%28+9+%29%29%2F2%5C1+=+-1

Quadratic expression 1x%5E2%2B-1x%2B-2 can be factored:
1x%5E2%2B-1x%2B-2+=+1%28x-2%29%2A%28x--1%29
Again, the answer is: 2, -1. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-1%2Ax%2B-2+%29



So the x-intercepts are (-1,0) and (2,0)

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B-3x%2B-9+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-3%29%5E2-4%2A2%2A-9=81.

Discriminant d=81 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--3%2B-sqrt%28+81+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-3%29%2Bsqrt%28+81+%29%29%2F2%5C2+=+3
x%5B2%5D+=+%28-%28-3%29-sqrt%28+81+%29%29%2F2%5C2+=+-1.5

Quadratic expression 2x%5E2%2B-3x%2B-9 can be factored:
2x%5E2%2B-3x%2B-9+=+2%28x-3%29%2A%28x--1.5%29
Again, the answer is: 3, -1.5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-3%2Ax%2B-9+%29



So the x-intercepts are (-1.5,0) and (3,0)