Anna knits pairs of mittens and scarves. She knits at most 18 pairs of mittens and 12 scarves each month. She has enough yarn to knit 24 items per month. Each pair of mittens sold earns a profit of $3 and each scarf sold earns a profit of $4. How many pairs of mittens and scarves should Anna knit in order to maximize her profit? 18 pairs of mittens and 6 scarves

12 pairs of mittens and 12 scarves

0 pairs of mittens and 24 scarves

24 pairs of mittens and 0 scarves

the answer to your question (9+10) is 19

(a) x intercepts: -6 and 2

you can obtain these by solving the equation 0=x^2 +4x-12 using your favorite quadratic formula. but it is easy to verify -6 and 2 indeed satisfy this equation.

(b) y intercept: -12

this is obtained by setting x=0: 0^2+4*0-12 = -12

(c) the minimum value is: -16 (this is the vertex)

you can get the vertex by rewriting the equation into the form:

there is no global or local maximum as the function goes to infinity, so only in the limit sense: +infinity.