SOLUTION: I know that the fomula x= -b/2a is used to solve for the minimum/maximum value of a quadratic formula but what happens when the quadratic formula is {{{ y= -6x^2-1 }}} a= -6 b=0(?

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: I know that the fomula x= -b/2a is used to solve for the minimum/maximum value of a quadratic formula but what happens when the quadratic formula is {{{ y= -6x^2-1 }}} a= -6 b=0(?      Log On


   

Question 341980: I know that the fomula x= -b/2a is used to solve for the minimum/maximum value of a quadratic formula but what happens when the quadratic formula is +y=+-6x%5E2-1+ a= -6 b=0(?) c= -1. I know that the maximum value= -1 but I dont understand how to solve for it. Please Help Me. Thanks in advance for your help and glorious time.
- Kay
Found 2 solutions by jim_thompson5910, robertb:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
You are correct. The value of b is b=0 since +y=+-6x%5E2-1+ is the same as +y=+-6x%5E2%2B0x-1+


So the x coordinate of the vertex is x=-b%2F2a=-0%2F%282%28-6%29%29=0


Plug this back in to get y=-6%280%29%5E2-1=-1. So the vertex is (0, -1)


So you are correct. The max value is -1.


To solve +y=+-6x%5E2-1+, plug in y=0 to get +0=+-6x%5E2-1+



Notice that the quadratic -6x%5E2-1 is in the form of Ax%5E2%2BBx%2BC where A=-6, B=0, and C=-1


Let's use the quadratic formula to solve for "x":


x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


x+=+%28%280%29+%2B-+sqrt%28+%280%29%5E2-4%28-6%29%28-1%29+%29%29%2F%282%28-6%29%29 Plug in A=-6, B=0, and C=-1


x+=+%280+%2B-+sqrt%28+0-4%28-6%29%28-1%29+%29%29%2F%282%28-6%29%29 Square 0 to get 0.


x+=+%280+%2B-+sqrt%28+0-24+%29%29%2F%282%28-6%29%29 Multiply 4%28-6%29%28-1%29 to get 24


x+=+%280+%2B-+sqrt%28+-24+%29%29%2F%282%28-6%29%29 Subtract 24 from 0 to get -24


x+=+%280+%2B-+sqrt%28+-24+%29%29%2F%28-12%29 Multiply 2 and -6 to get -12.


x+=+%280+%2B-+2i%2Asqrt%286%29%29%2F%28-12%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%280%2B2i%2Asqrt%286%29%29%2F%28-12%29 or x+=+%28-0-2i%2Asqrt%286%29%29%2F%28-12%29 Break up the expression.


x+=+-%28i%2Asqrt%286%29%29%2F%286%29 or x+=+%28i%2Asqrt%286%29%29%2F%286%29 Reduce and simplify


So the solutions are x+=+-%28i%2Asqrt%286%29%29%2F%286%29 or x+=+%28i%2Asqrt%286%29%29%2F%286%29


If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim

Answer by robertb(5830) About Me  (Show Source):