Question

Let g(x) = -x² - 2x + 5 and h(x) be another function. What could be a possible form for h(x) to complete this equation: h(x) = g(x) + c?

a) c is a constant
b) c is a linear function
c) c is a quadratic function
d) c is an exponential function

Answer 1

To complete the equation h(x)=g(x)+c, a possible form for c is a quadratic function (Option C).

Step-by-step explanation:

Given g(x) = -x^2−2x+5, the sum of g(x) and a quadratic function c would yield h(x)= −x^2 −2x+5+c. A quadratic function involves terms up to x^2, making it compatible with this expression. On the contrary, linear and exponential functions would introduce terms beyond quadratic, altering the form of the equation. Therefore, c being a quadratic function ensures compatibility with the given expression, making Option C the correct answer.