Y equals -2x2-8x plus 1 solve by completing the square?

Answer 1

-2x^2 - 8x + 1 = 0

x^2 + 4x - 1/2 = 0

x^2 + 4x = 1/2

x^2 + 4x + 4 = 9/2

(x + 2)^2 = 9/2

x + 2 = ±√(9/2)

x = ±√[(9)(2)/(2)(2)] - 2

x = ±(3/2)√2 - 2

x = (3/2)√2 - 2 or x = -(3/2)√2 - 2

Check:

-2x^2 - 8x + 1 = 0

-2[(3/2)√2 - 2]^2 - 8[(3/2)√2 - 2] + 1 =? 0

-2(9/2 - 6√2 + 4) - 12√2 + 16 + 1 =? 0

-9 + 12√2 - 8 - 12√2 + 16 + 1 =? 0

-17 + 17 =? 0

0 = 0 True

-2x^2 - 8x + 1 = 0

-2[-(3/2)√2 - 2]^2 - 8[-(3/2)√2 - 2] + 1 =? 0

-2[-[(3/2)√2 + 2]]^2 - 8[-(3/2)√2 - 2] + 1 =? 0

-2(9/2 + 6√2 + 4) + 12√2 + 16 + 1 =? 0

-9 - 12√2 - 8 + 12√2 + 16 + 1 =? 0

-17 + 17 =? 0

0 = 0 True

Answer 2

To solve the quadratic equation y = -2x^2 - 8x + 1 by completing the square, follow these steps:

1. Move the constant term (1) to the right side of the equation: y - 1 = -2x^2 - 8x.
2. Divide the equation by the coefficient of x^2 (-2): (y - 1)/(-2) = x^2 + 4x.
3. Complete the square by adding (4/2)^2 = 4 to both sides of the equation: (y - 1)/(-2) + 4 = x^2 + 4x + 4.
4. Simplify: (y - 1)/(-2) + 4 = (x + 2)^2.
5. Rewrite the equation in the vertex form: (y - 1)/(-2) = (x + 2)^2 - 4.
6. The vertex form is y = a(x - h)^2 + k, where (h, k) represents the vertex. Here, the vertex is (-2, -4).