SOLUTION: If there is only one solution to the equation 0= -x^2 + bx -8 what are the possible values of b?

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Question 1010344: If there is only one solution to the equation 0= -x^2 + bx -8 what are the possible values of b?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+0+=+-x%5E2+%2B+b%2Ax+-+8+
One solution means this parabola touches the
x-axis at one point
The quadratic formula is:
+x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
Just get rid of the part that gives 2 solutions,
the +- part.
+x+=+%28-b+%29%2F%282%2Aa%29+
+x+=+%28-b%29%2F%28-2%29+
+x+=+b%2F2+
--------------
+0+=+-%28b%2F2%29%5E2+%2B+b%2A%28b%2F2%29+-+8+
+0+=+-b%5E2%2F4+%2B+b%5E2%2F2+-+8+
+0+=+b%5E2%2F4+-+8+
+b%5E2%2F4+=+8+
+b%5E2+=+32+
+b+=+4%2Asqrt%282%29+
+b+=+-4%2Asqrt%282%29+
-----------------
check the answers:
+sqrt%28+b%5E2-4%2Aa%2Ac+%29+ must equal zero, so
+b%5E2+=+4a%2Ac+
+%28+4%2Asqrt%282%29+%29%5E2+=+4%2A%28+-1+%29%2A%28-8%29+
+16%2A2+=+32+
+32+=+32+
and
+b%5E2+=+4a%2Ac+
+%28+-4%2Asqrt%282%29+%29%5E2+=+4%2A%28+-1+%29%2A%28-8%29+
+16%2A2+=+32+
+32+=+32+
OK
Here is the plot:
+graph%28+400%2C+400%2C+-2%2C+10%2C+-10%2C+2%2C+-x%5E2+%2B+4%2Asqrt%282%29%2Ax+-+8+%29+