Question 43680
{{{4x^2 + 4y^2 + 4y = 15}}}
{{{4(x^2 + 0x) + 4(y^2 + y) = 15}}}
{{{4(x + 0)^2 + 4(y + (1/2))^2 = 15 + 1}}}
{{{4(x + 0)^2 + 4(y + (1/2))^2 = 16}}}
{{{(x + 0)^2 + (y + (1/2))^2 = 4}}}
a) This is a circle.
b) Does not open.
c) V(0,-0.5)
d) Axis of Symmetry: {{{y=-0.5}}} and {{{x=0}}}
e) X-Intercept
{{{(x + 0)^2 + (y + (1/2))^2 = 4}}}
{{{(x + 0)^2 + (0 + (1/2))^2 = 4}}}
{{{x^2 + (1/4) = 4}}}
{{{x^2 = 15/4}}}
{{{x = +- sqrt(15)/2}}}
f) Y-Intercept
{{{(0 + 0)^2 + (y + (1/2))^2 = 4}}}
{{{(y + (1/2))^2 = 4}}}
{{{y + (1/2) = +- 2}}}
{{{y = -0.5 +- 2}}}
You can fill in the table of values.
h) graph
{{{ graph( 300, 300, -5, 5, -5, 5, -0.5 + sqrt(4 - x^2), -0.5 - sqrt(4 - x^2), -0.5 ) }}}