How do i get g(x+a)-g(x)

Question

G(x)=-4x²+5x

Answer 1

g(x)=-4x^2+5x

replace x by x+a

g(x+a) = -4(x+a)^2 +5(x+a)

= -4x^2-8ax-4a^2 +5x +5a

g(x+a)-g(x)= -4x^2 -8ax -4a^2 +5x +5a -(-4x^2 +5x)

=- 8ax -4a^2 +5a

Answer 2

For finding the value of the function at any point, we plus that point in place of x.

For eg in the function above g(x) = - 4x^2+5x

if we have to find g(point) = -4 (point) ^2 + 5*point

In the above ques, g(x+a) = -4(x+a)^2 + 5(x+a)

=-4(x^2 + 2xa + a^2) +5x + 5a

= -4x^2 -8xa - 4a^2 +5x + 5a

Calculating, g(x+a) - g(x) = {-4x^2 -8xa - 4a^2 +5x + 5a} - {- 4x^2+5x}

= 4x^2 -8xa - 4a^2 +5x + 5a+4x^2-5x

= -8xa - 4a^2 +5a