## Algebra 1

a) The graph was made using graphing software. b) $y=135-x^2$ $0 = 135-x^2$ $x^2= 135-x^2+x^2$ $x^2 = 135$ $\sqrt {x^2} = \sqrt {135}$ $x = 11.6189, -11.6189$ We cannot have a negative sidelength, so $x=11.6189$. (We cannot have a negative area, so the maximum value for $x$ was 11.6189.) c) The range of the function is the possible y-values. Since there cannot be a negative area, the lowest value for the range is 0. d) $117 = 135-x^2$ $117-117+x^2 = 135-x^2-117+x^2$ $x^2 = 18$ $\sqrt {x^2} = \sqrt {18}$ $x = 4.2426, -4.2426$ We cannot have a negative sidelength, so $x=4.2426$.