SOLUTION: What is the vertex of the parabola f(x)=-2(x-7)^2-4??

Algebra ->  Graphs -> SOLUTION: What is the vertex of the parabola f(x)=-2(x-7)^2-4??      Log On


   

Question 1111544: What is the vertex of the parabola f(x)=-2(x-7)^2-4??
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+f%28x%29+=+-2%2A%28+x-7+%29%5E2+-+4+
+f%28x%29+=+-2%2A%28+x%5E2+-+14x+%2B+49+%29+-+4+
+f%28x%29+=+-2x%5E2+%2B+28x+-+98+-+4+
+f%28x%29+=+-2x%5E2+%2B+28x+-+102+
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The formula for the x-value of the vertex is:
+x%5Bv%5D+=+-b%2F%282a%29+
when the form is:
+f%28x%29+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+
----------------------------------
+x%5Bv%5D+=+-28%2F%282%2A%28-2%29+%29+
+x%5Bv%5D+=+7+
Plug this result back into the equation
+f%287%29+=+-2%2A7%5E2+%2B+28%2A7+-+102+
+f%287%29+=+-98+%2B+196+-+102+
+f%287%29+=+-4+
The vertex is at ( 7, -4 )
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check:
Here's the plot:
+graph%28+400%2C+400%2C+-5%2C+10%2C+-20%2C+2%2C+-2x%5E2+%2B+28x+-+102+%29+
Looks correct