SOLUTION: How many times will the graph of y=5x^2-1 intersect: (a) The x-axis? (b) The y- axis? Thank You!

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Question 718182: How many times will the graph of y=5x^2-1 intersect: (a) The x-axis? (b) The y- axis? Thank You!
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
It can intersect the y-axis either:
(a) once
(b) not at all
If it intersected more than once, that would violate the
definition of a function, which needs 1 unique value of
+y+ for each +x+
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In this case, set +x+=+0+ to find y-crossing
+y+=+5x%5E2+-+1+
+y+=+5%2A0+-+1+
+y+=+-1+
so, the y-crossing is at (0,-1)
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The x-crossing(s) is where +y+=+0+, and there can be
(a) none
(b) one
(c) two
for a 2nd degree equation, which is what this is.
In this case there are 2 x-crossings
+0+=+5x%5E2+-+1+
+5x%5E2+=+1+
+x%5E2+=+1%2F5+
+x+=+1%2Fsqrt%285%29+
+x+=+-1%2Fsqrt%285%29+
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