It is known that the quadratic function y = 2x ^ 2 + 9x + 34, when the independent variable x takes two different values X1 and X2, the function values are equal, then the function values when the independent variable x takes X1 + x2 are equal to the function values when x is the value

It is known that the quadratic function y = 2x ^ 2 + 9x + 34, when the independent variable x takes two different values X1 and X2, the function values are equal, then the function values when the independent variable x takes X1 + x2 are equal to the function values when x is the value

y=2x^2+9x+34
y=2(x+9/4)^2+191/8
Axis of symmetry: x = - 9 / 4
Apex: 191 / 8
As long as the distance between X1 and X2 - 9 / 4 is equal, the function value will be equal
That is: X1 - (- 9 / 4) = (- 9 / 4) - x2
The result is: X1 + x2 = - 9 / 2
When the independent variable x takes X1 + X2, the function value:
y=2*(-9/2)^2+9*(-9/2)+34
=34