An arch way is modeled by the equation y=-2x^2+8x. a rod is to be placed across the archway at an angle definded by the equation x-2.23y+10.34=0. if the rod is attached to the archway at points a and b, such that point b is at a higher level than point a, at what distance from the ground is point b ?

So.. hmm check the picture below

now, to know where A and B are, that occurs when the parabolic equation equates the linear one

thus 



now, running that on the quadratic formula, you end up with the values of 3.00402497440839842242  and 0.77175977895483027713

thus B rounded up is 3.004  and A rounded up is 0.7718

what's the "y" value for B?, well, you can use either the linear or quadratic equation for that, let's use the quadratic one