Convert into vertex form?

Question

-2x^2-8x+4

Answer 1

Given quadratic function f(x) = - 2x ² - 8x + 4

Standard form of parabola y  = ax ² + bx + c

Vertex form of parabola is y  = a (x - h ) ² + k

Here x ² coefficient is -2 , for perfect square make x ² coefficient 1 by dividing each side by negitive 2.

y/-2  = x ² + 4x  - 2

To complete the squre add (half cooefficient of x ) ² to each side of the expression.

x  coefficient = 4 then (half the x coefficient)² is (2) ² = 4.

.y/-2 + 4 =  x ² + 4x + 4  - 2

y/-2  =  x ² + 4x + 4 - 4  - 2

y/-2  = (x ² + 4x + 4 ) - 6

y/-2 =  (x + 2) ² - 6

y  = - 2 (x - (-2)) ² + 12

Now which is in vertex  form y  = a (x - h ) ² + k.

Vertex (h ,k ) = (-2, 12 ), a = -2.