SOLUTION: what is the vertex and line of semmetry of f(x)=-3(x+2)^2 graph the function thanks in advance solve for x 4x^2=-9x-2 solve by completing the square x^2 + 13/2x =13

Algebra ->  Linear-equations -> SOLUTION: what is the vertex and line of semmetry of f(x)=-3(x+2)^2 graph the function thanks in advance solve for x 4x^2=-9x-2 solve by completing the square x^2 + 13/2x =13       Log On


   

Question 320057: what is the vertex and line of semmetry of f(x)=-3(x+2)^2
graph the function
thanks in advance

solve for x
4x^2=-9x-2
solve by completing the square
x^2 + 13/2x =13
the width of a rectangle is 2ft less . the area is 15ft^2. find the lenghth and width...
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The equation is already in vertex form, y=a%28x-h%29%5E2%2Bk, where (h,k) is the vertex.
Comparing
f%28x%29=-3%28x%2B2%29%5E2
f%28x%29=-3%28x%2B2%29%5E2%2B0
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(h,k)=(-2,0).
The axis of symmetry includes the vertex.
x=-2
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4x%5E2=-9x-2
4x%5E2%2B9x%2B2=0
4%28x%5E2%2B%289%2F4%29x%29%2B2=0
4%28x%5E2%2B%289%2F4%29x%2B81%2F64%29%2B2-81%2F16=0
4%28x%2B9%2F8%29%5E2-49%2F16=0
4%28x%2B9%2F8%29%5E2=49%2F16
%28x%2B9%2F8%29%5E2=49%2F64
x%2B9%2F8=0+%2B-+7%2F8
x=-9%2F8+%2B-+7%2F8
highlight%28x=-2%29 and highlight%28x=-1%2F4%29
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x%5E2+%2B+%2813%2F2%29x+=13
x%5E2+%2B+%2813%2F2%29x+%2B%2813%2F4%29%5E2=13%2B%2813%2F4%29%5E2
%28x%2B%2813%2F4%29%29%5E2=208%2F16%2B169%2F16
%28x%2B%2813%2F4%29%29%5E2=377%2F16
x%2B13%2F4=0+%2B-+sqrt%28377%29%2F4
highlight%28x=-13%2F4+%2B-+sqrt%28377%29%2F4%29
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For a rectangle,
A=L%2AW=15
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W=L-2
Substitute,
L%2A%28L-2%29=15
L%5E2-2L=15
L%5E2-2L-15=0
%28L-5%29%28L%2B3%29=0
Only the positive solution makes sense in this problem,
L-5=0
highlight%28L=5%29
Then,
W=L-2
W=5-2
highlight%28W=3%29