Question 464434
1.

*[tex \LARGE -2(x+6)^2 + 14 = 14]


*[tex \LARGE -2(x+6)^2 = 0]


*[tex \LARGE (x+6)^2 = 0]


*[tex \LARGE x = -6]


2. f(-6) = 14, so (-6, 14).


3. Set f(x) equal to 0:


*[tex \LARGE -2(x+6)^2 + 14 = 0]


*[tex \LARGE (x+6)^2 = 7]


*[tex \LARGE x+6 = \pm \sqrt{7}]


*[tex \LARGE x = -6 \pm \sqrt{7}], so x intercepts are *[tex (-6 + \sqrt{7},0)] and *[tex (-6 - \sqrt{7}, 0)]


4. Replace x with 0 to find the y-intercept.


*[tex \LARGE f(0) = -2(0+6)^2 + 14 = -58], y-intercept is (0,-58). Note that polynomial functions are defined everywhere so the conditional "if there is one" is meaningless, all polynomial functions will have a y-intercept.