Question

1. The sum of the squares of two numbers is 74 and the difference of their squares is 24.
a) What system of equations models this situation?
b) What are the two numbers?

2. For what value of b will the line y= -2x+b be tangent to the parabola y=3x^2+4x-1?

Answer 1

(x+y)(x-y) = 24
x^2+y^2 = 74

you want some place where the tangent to the parabola has slope = -2

6x+4 = -2
x = -1
so, y=-2
The tangent line at (-1,-2) is
y+2 = -2(x+1)
y = -2x-4
b = -4

see

http://www.wolframalpha.com/input/?i=plot+y%3D3x^2%2B4x-1%2C+y+%3D+-2x-4