Convert the quadratic function y=-2x2 -16x-37
3 years ago
I'm assuming you want it converted from this form to vertex form. We need to get there by completing the square
y = -2(x2 + 8x + 37/2) --> I factored out -2
y = -2(x2 + 8x + 42 - 42 + 37/2) --> complete square with (8/2)2
Note: we have to add AND subtract it so we don't change the final value of our equation
y = -2([x2 + 8x + 16] - 42 + 37/2) --> factor the first part of this into a binomial
y = -2 ((x+4)(x+4) - 42 + 37/2) --> (x+4)(x+4) can be rewritten as (x+4)2
y = -2[(x+4)2 - 16 + 37/2] --> expand so we have fewer brackets
y = -2(x+4)2 - 32 + 37 --> simplify
y = -2(x+4)2 + 5 --> we did it!
Hopefully that makes sense but if not, feel free to ask more questions!
Woah I made a mistake there at the end! The last two lines should read:
y = -2(x+4)2 + 32 - 37
y = -2(x+4)2 - 5
my bad
3 years ago
Answered By Emily D
I'm assuming you want it converted from this form to vertex form. We need to get there by completing the square
y = -2(x2 + 8x + 37/2) --> I factored out -2
y = -2(x2 + 8x + 42 - 42 + 37/2) --> complete square with (8/2)2
Note: we have to add AND subtract it so we don't change the final value of our equation
y = -2([x2 + 8x + 16] - 42 + 37/2) --> factor the first part of this into a binomial
y = -2 ((x+4)(x+4) - 42 + 37/2) --> (x+4)(x+4) can be rewritten as (x+4)2
y = -2[(x+4)2 - 16 + 37/2] --> expand so we have fewer brackets
y = -2(x+4)2 - 32 + 37 --> simplify
y = -2(x+4)2 + 5 --> we did it!
Hopefully that makes sense but if not, feel free to ask more questions!
3 years ago
Answered By Emily D
Woah I made a mistake there at the end! The last two lines should read:
y = -2(x+4)2 + 32 - 37
y = -2(x+4)2 - 5
my bad