SOLUTION: I need to solve this where the x- intercepts please help y=-x^2+6x-2

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Question 88998This question is from textbook algebra
: I need to solve this where the x- intercepts
please help
y=-x^2+6x-2 This question is from textbook algebra

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Now let's use the quadratic formula to solve for x:


Starting with the general quadratic

ax%5E2%2Bbx%2Bc=0

the general solution using the quadratic equation is:

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29

So lets solve -x%5E2%2B6%2Ax-2=0 ( notice a=-1, b=6, and c=-2)

x+=+%28-6+%2B-+sqrt%28+%286%29%5E2-4%2A-1%2A-2+%29%29%2F%282%2A-1%29 Plug in a=-1, b=6, and c=-2



x+=+%28-6+%2B-+sqrt%28+36-4%2A-1%2A-2+%29%29%2F%282%2A-1%29 Square 6 to get 36



x+=+%28-6+%2B-+sqrt%28+36%2B-8+%29%29%2F%282%2A-1%29 Multiply -4%2A-2%2A-1 to get -8



x+=+%28-6+%2B-+sqrt%28+28+%29%29%2F%282%2A-1%29 Combine like terms in the radicand (everything under the square root)



x+=+%28-6+%2B-+2%2Asqrt%287%29%29%2F%282%2A-1%29 Simplify the square root



x+=+%28-6+%2B-+2%2Asqrt%287%29%29%2F-2 Multiply 2 and -1 to get -2

So now the expression breaks down into two parts

x+=+%28-6+%2B+2%2Asqrt%287%29%29%2F-2 or x+=+%28-6+-+2%2Asqrt%287%29%29%2F-2


which split up to


x=-6%2F-2%2B2%2Asqrt%287%29%2F-2 or x=-6%2F-2-2%2Asqrt%287%29%2F-2


and simplify to


x=3-1%2Asqrt%287%29 or x=3%2B1%2Asqrt%287%29


Which approximate to

x=0.354248688935409 or x=5.64575131106459


So our solutions are:
x=0.354248688935409 or x=5.64575131106459

Notice when we graph -x%5E2%2B6%2Ax-2, we get:



when we use the root finder feature on a calculator, we find that x=0.354248688935409 and x=5.64575131106459.So this verifies our answer