Question

If g(x) = 2x^2 + x - 7, evaluate g(a + b).

a. 2(a + b)^2 - 7
b. 2a^2 + 2b^2 + a + b - 7
c. 2a^2 + 4ab + 2b^2 + a + b - 7
d. 2a^2b^2 + a + b - 7

Answer 1

To evaluate g(a + b) for the quadratic function g(x) = 2x^2 + x - 7, we substitute and expand the expression. After expanding and simplifying, we find that the correct evaluation of g(a + b) is c. 2a^2 + 4ab + 2b^2 + a + b - 7.

Step-by-step explanation:

To evaluate g(a + b) for the function g(x) = 2x2 + x - 7, we substitute x with (a + b) and expand the expression:

g(a + b) = 2(a + b)2 + (a + b) - 7

Now, we expand (a + b)2 which is equal to a2 + 2ab + b2. Substituting this into our expression gives:

g(a + b) = 2(a2 + 2ab + b2) + a + b - 7

Distribute the 2 to each term inside the parenthesis:

g(a + b) = 2a2 + 4ab + 2b2 + a + b - 7

Thus, the correct expression is c. 2a2 + 4ab + 2b2 + a + b - 7.