x-intercepts of f(x) are
[tex]f(x)=(x+3)^{2}-1=0 [/tex]
[tex] x_{1}= -2, x_{2}=-4 [/tex]
As points they are (-2,0) and (-4,0)
y-intercept of f(x) is
[tex]f(0)=(0+3)^{2}-1=8 [/tex]
As a point it is (0,8)
x-intercepts of g(x) are:
[tex]g(x)=-2 x^{2} +8x+3=0[/tex]
[tex] x_{1}= \frac{-4+ \sqrt{22} }{-2} , x_{2}= \frac{-4- \sqrt{22} }{-2} [/tex]
y-intercept of g(x) is:
[tex]g(0)=-2*0+8*0+3=3[/tex]
As a point it is (0,3)
f(x) has a minima, the function is cap-sized. Since we have a simple case of quadratic function, there is no need to check the second order derivative. Indeed, I will attach both graphs for f(x) and g(x). The minima of f(x) is (-3,-1). And g(x) has a maxima. This maxima is the point (2,11)
