SOLUTION: the graph of the equation y=x^2+2x-8 where does it intersect the x-axis?

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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.
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
To find the x-intercepts, we need to factor
Solved by pluggable solver: Factoring Quadratics with a leading coefficient of 1 (a=1)
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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