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Quadratic function of high school mathematics
The quadratic function of 1) has two zeros and -2, and the minimum value of f(x) is-1, so suppose that y = a (x-b) 2- 1, where a >;; 0

By introducing coordinates (0,0) and (-2,0), a = 1 and b =- 1 are obtained.

So y = (x+ 1) 2- 1 = x 2+2x.

2)

h(x)=f(X)+λf(-x)=x? +2x+

1+λ(x? -2x)=( 1+λ)x? +(2-2λ)x

The new function increments at-1 And 1.

It holds when 1+λ=0 and λ=- 1

(λ- 1)/(λ+ 1)> 1, λ

When 1+λ >; 0,(λ- 1)/(λ+ 1)