SOLUTION: Could you help me find the x-intercepts of the equation y=-2x^2-8x+20?

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Question 29077: Could you help me find the x-intercepts of the equation y=-2x^2-8x+20?

Found 2 solutions by venugopalramana, mathtech5:
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
Could you help me find the x-intercepts of the equation y=-2x^2-8x+20?
X INTERCEPT MEANS THE X COORDINATE OF THE POINT/POINTS , WHERE THE GRAPH CUTS X AXIS...THAT IS WHERE Y COORDINATE IS ZERO...SO PUT Y=0 AND FIND X VALUES.HERE WE HAVE
-2x^2-8x+20=0...OR......X^2+4X-5=0
X^2+5X-X-5=0
X(X+5)-1(X+5)=0
(X-1)(X+5)=0
X=1 AND X=-5 ...SO THE X INTERCEPTS ARE +1 AND - 5

Answer by mathtech5(4) About Me  (Show Source):
You can put this solution on YOUR website!
The x-intercepts occur when the value of y is zero.
When trying to solve any equation - the first thing we should do is try to pull out what the terms have in common (if possible). For this equation, we can pull out (or factor out) a -2 to get:
y = -2(x^2 + 4x - 10)
Next we see if the expression within the parenthesis can be factored (by a reverse FOIL method). This expression can not be factored. We can not find factors of 10 that subtract to be 4. So we must use the quadratic formula:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B4x%2B-10+=+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=%284%29%5E2-4%2A1%2A-10=56.

Discriminant d=56 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-4%2B-sqrt%28+56+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%284%29%2Bsqrt%28+56+%29%29%2F2%5C1+=+1.74165738677394
x%5B2%5D+=+%28-%284%29-sqrt%28+56+%29%29%2F2%5C1+=+-5.74165738677394

Quadratic expression 1x%5E2%2B4x%2B-10 can be factored:
1x%5E2%2B4x%2B-10+=+1%28x-1.74165738677394%29%2A%28x--5.74165738677394%29
Again, the answer is: 1.74165738677394, -5.74165738677394. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B4%2Ax%2B-10+%29



REMEMBER: you can always check your solutions by plugging the number back into the equation. Since the solutions are decimals, the number you get when you plug in the solution will be close to zero.