# 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-12

1 answer

###### Question:

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-12

(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-12

## Answers

Answer:The vertex is the point (1,-8)Step-by-step explanation:we have[tex]y=-4x^{2} +8x-12[/tex]Convert to vertex formstep 1Group terms that contain the same variable, and move the constant to the opposite side of the equation[tex]y+12=-4x^{2} +8x[/tex]step 2Factor the leading coefficientfactor -4[tex]y+12=-4(x^{2} -2x)[/tex]step 2Complete the square. Remember to balance the equation by adding the same constants to each side[tex]y+12-4=-4(x^{2} -2x+1)[/tex][tex]y+8=-4(x^{2} -2x+1)[/tex]step 3Rewrite as perfect squares[tex]y+8=-4(x-1)^{2}[/tex]thereforeThe vertex is the point (1,-8)

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