SOLUTION: Plot these two functions on the same axes: y = (x + 3)^2 and y = -2 x + 10 Visually

Algebra ->  Inequalities -> SOLUTION: Plot these two functions on the same axes: y = (x + 3)^2 and y = -2 x + 10 Visually      Log On


   



Question 1084163: Plot these two functions on the same axes:

y = (x + 3)^2
and
y = -2 x + 10
Visually inspect the graph. Estimate where (in terms of x) the linear equation is less than the quadratic equation. Express your answer as an interval or an inequality.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+y+=+%28+x+%2B+3+%29%5E2+
+y+=+-2x+%2B+10+
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Here is the plot:
+graph%28+400%2C+400%2C+-10%2C+10%2C+-10%2C+50%2C+%28+x+%2B+3+%29%5E2%2C+-2x+%2B+10+%29+
-----------------------
The line is less than the quadratic when:
+%28+x+%2B+3+%29%5E2+%3E+-2x+%2B+10+
+x%5E2+%2B+6x+%2B+9+%3E+-2x+%2B+10+
+x%5E2+%2B+8x+%3E+1+
complete the square
+x%5E2+%2B+8x+%2B+4%5E2+%3E+1+%2B+4%5E2+
+%28+x+%2B+4+%29%5E2+%3E+17+
Take the square root of bpth sides
+x+%2B+4+%3E+4.1231+
+x+%3E+.1231+
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Plug result back into either equation
+y+=+-2x+%2B+10+
+y+=+-2%2A.1231+%2B+10+
+y+=+10+-+.24621+
+y+=+9.7538+ when +x+=+.1231+