SOLUTION: Write the quadratic function in the form y = a(x - h)2 + k. Find the veertex, axis of symmetry, domain and range
y = -2x2 - 8x - 5
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Question 316858: Write the quadratic function in the form y = a(x - h)2 + k. Find the veertex, axis of symmetry, domain and range
y = -2x2 - 8x - 5
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Factor out -2 from the variable terms:
 -\ 5)
Divide the coefficient on the 
term by 2 and square the result. ^2\ =\ 4)
Add 4 inside the parentheses and (4)\ =\ 8)
outside the parentheses
 -\ 5\ +\ 8)
\ +\ 3)
Factor the perfect square in the parentheses:
^2\ +\ 3)
Vertex: )
Axis of symmetry: 
Domain: (All real numbers, just like any other polynomial function) 
Range: The lead coefficient is negative, therefore the parabola opens downward and the vertex represents a maximum value of the function. That maximum value is the 
-coordinate of the vertex, namely 
. The range is unconstrained less than the maximum, so Range: 
You didn't ask for the intercepts, but here they are anyway:
The -intercept is at the value of the function when 
, so:
\ =\ -2(0)^2\ -\ 8(0)\ -\ 5\ =\ -5)
and the -intercept is )
The -intercepts are the roots of:
Verification of that last step is left as an exercise for the student.
Hence the -intercepts are )
and )
John
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