for 1a,
set x=0 to find y-intercept.
set y=0 to find x-intercept.
the function is a positive parabola and is shown in the first image.
for 1b,
same process, similar looking graph shown in the second image.
for 2,
[tex]area = 4\pi {r}^{2} = 196\pi \: {in}^{2} [/tex]
[tex] {r}^{2} = 49 \: {in}^{2} [/tex]
[tex]r = 7 \: in[/tex]
for 3, (refer to third image)
we'll use Pythagorean theorem
[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]
[tex] {x}^{2} + {(2x)}^{2} = {h}^{2} [/tex]
simplify and put it into a standard form:
[tex] 5{x}^{2} = 45[/tex]
quadratic equation:
[tex] {x}^{2} - 9 = 0[/tex]
then solve for x:
[tex]x = \sqrt{9} = 3cm[/tex]
so one leg is 3cm
the other is two times that (6cm)
