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Use the method of completing the square to write the equations of the given parabola in this form: (y-k)=a(x-h)^2 where a =0, (h,k) is the vertex, and x=h is the axis of symmetry. Find the vertex of this parabola: y=-4x^2-8x-7

User HMT
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1 Answer

4 votes

Answer:

(-1, -3)

Explanation:


(y-k)=a(x-h)^2,\ a\\eq0


(a\pm b)^2=a^2\pm2ab+b^2\qquad(*)

We have


y=-4x^2-8x-7


y=-4x^2-4(2x)-4(1)-3

distribute


y=-4(\underbrace{x^2+2x+1}_((*)))-3

use (*)


y=-4(x+1)^2-3

add 3 to both sides


y+3=-4(x+1)^2


y-(-3)-4\bigg(x-(-1)\bigg)^2

the vertex


(-1;\ -3)

User Rennie
by
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