Answer
a) 7.4 $units^2$
b) 7.8 $units^2$
c) $(1.61, 3.22)$, $(1.61, -3.22)$, $(-1.61, 3.22)$, $(-1.61, -3.22)$
d) 10.37 $units^2$
Work Step by Step
a)
length of base is 2 units
$y=-.3x^2+4$
$y=-.3(1)^2+4$
$y=-.3*1+4$
$y=-.3+4$
$y=3.7$
$3.7*2 = 7.4$ $units^2$
b)
length of base is 6 units
$y=-.3x^2+4$
$y=-.3(3)^2+4$
$y=-.3*9+4$
$y=-2.7+4$
$y=1.3$
$6*1.3 = 7.8$ $units^2$
c) Since we are looking for a square, we have to set two equations equal to each other.
$y=2x$
$y=-.3x^2+4$
$2x=-.3x^2+4$
$.3x^2+2x-4=0$
$10*(.3x^2+2x-4=0)$
$3x^2+20x-40=0$
$x=(-b±\sqrt {b^2-4ac})/2a$
$x=(-20±\sqrt {20^2-4*3*-40})/2*3$
$x=(-20±\sqrt {400+480})/6$
$x=(-20±\sqrt {880})/6$
$x=(-20±29.66)/6$
$x=(-20+29.66)/6$
$x=9.66/6$
$x=1.61$
$x=(-20-29.66)/6$
$x=-49.66/6$
$x=-8.28$ (we can't have a negative length, so this answer is invalid)
$x=1.61$
$y=2x$
$y=2*1.61$
$y=3.22$
$(1.61, 3.22)$
Since the square is symmetric, we can find the other three points to be $(1.61, -3.22)$, $(-1.61, 3.22)$, and $(-1.61, -3.22)$
d)
$1.61-(-1.61) = 3.22$
$3.22*3.22 = 10.37$
