SOLUTION: Use the discriminant to determine the number of x-intercepts of the graph of the equation. y = x^2 − 14x + 49 ........... x-intercept(s)

Algebra ->  Graphs -> SOLUTION: Use the discriminant to determine the number of x-intercepts of the graph of the equation. y = x^2 − 14x + 49 ........... x-intercept(s)      Log On


   

Question 1076254: Use the discriminant to determine the number of x-intercepts of the graph of the equation.
y = x^2 − 14x + 49
........... x-intercept(s)
Found 2 solutions by josgarithmetic, josmiceli:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
y=x%5E2-14x%2B49

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y=ax%5E2%2Bbx%2Bc has discriminant b%5E2-4ac.
Your equation has system%28a=1%2Cb=-14%2Cc=49%29; just substitute and evaluate the discriminant.
.
.
.
ONE x-intercept.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The discriminant is +b%5E2+-+4%2Aa%2Ac+
+a+=+1+
+b+=+-14+
+c+=+49+
+b%5E2+-+4%2Aa%2Ac+=+%28-14%29%5E2+-+4%2A1%2A49+
+b%5E2+-+4%2Aa%2Ac+=+196+-+196+
+b%5E2+-+4%2Aa%2Ac+=+0+
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The is one x-intercept at
+-b%2F%282a%29+=+-%28-14%29%2F%282%2A1%29+
+-b%2F%282a%29+=+7+
+x+=+7+
and
+y+=+x%5E2+-+14x+%2B+49+
+y+=+49+-+14%2A7+%2B+49+
+y+=+98+-+98+
+y+=+0+
( 7.0 ) is the x-intercept
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Here's a plot:
+graph%28+400%2C+400%2C+-2%2C+16%2C+-3%2C+16%2C+x%5E2+-+14x+%2B+49+%29+