simonjason491
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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

Respuesta :

gmany

Answer:

(-1, -3)

Step-by-step explanation:

[tex](y-k)=a(x-h)^2,\ a\neq0[/tex]

[tex](a\pm b)^2=a^2\pm2ab+b^2\qquad(*)[/tex]

We have

[tex]y=-4x^2-8x-7[/tex]

[tex]y=-4x^2-4(2x)-4(1)-3[/tex]

distribute

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

use (*)

[tex]y=-4(x+1)^2-3[/tex]

add 3 to both sides

[tex]y+3=-4(x+1)^2[/tex]

[tex]y-(-3)-4\bigg(x-(-1)\bigg)^2[/tex]

the vertex

[tex](-1;\ -3)[/tex]

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