Question 77254: the graph of the equation y=x^2+2x-8 where does it intersect the x-axis? Found 2 solutions by checkley75, jim_thompson5910:Answer by checkley75(3666) (Show Source):
You can put this solution on YOUR website! y=x^2+2x-8 (graph 300x200 pixels, x from -6 to 5, y from -10 to 10, y = 2x -8).
according to the graph it is +4 for the x intercept.
also if you set y=0 we get the same answer:
0=2x-8
2x=8
x=8/2
x=4 answer.
In order to factor , first we need to ask ourselves: What two numbers multiply to -8 and add to 2? Lets find out by listing all of the possible factors of -8
Factors:
1,2,4,8,
-1,-2,-4,-8,List the negative factors as well. This will allow us to find all possible combinations
These factors pair up to multiply to -8.
(-1)*(8)=-8
(-2)*(4)=-8
Now which of these pairs add to 2? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 2
First Number
|
Second Number
|
Sum
1
|
-8
|
|
1+(-8)=-7
2
|
-4
|
|
2+(-4)=-2
-1
|
8
|
|
(-1)+8=7
-2
|
4
|
|
(-2)+4=2
We can see from the table that -2 and 4 add to 2.So the two numbers that multiply to -8 and add to 2 are: -2 and 4
Now we substitute these numbers into a and b of the general equation of a product of linear factors which is:
substitute a=-2 and b=4
So the equation becomes:
(x-2)(x+4)
Notice that if we foil (x-2)(x+4) we get the quadratic again
So the equation becomes
Now let y=0
Set each factor equal to zero:
So the solutions are:
or
which means the x-intercepts are:
(2,0) and (-4,0)
graph of
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