Which graph can be used to find the solution(s) to 3 – 4x = –3 – x2 + 4x?

1. Consider the functions f(x)=-4x+3 and g(x)=

the graph of f is a line (f is a linear polynomial function) so we can use 2 points to draw it, say (0, 3) and (2, -5)

the graph of g is a parabola (g is a quadratic polynomial function), so we can factorize the expression as follows: 



so the roots of g are 1 and 3, the axis of symmetry is the vertical line through (2,0), so the vertex is calculated at x=2, -(2-3)(2-1)=-(-1)(1)=1. Vertex is the point (2, 1)

2. check the picture attached. Clearly there are 2 solutions, at the 2 intersections of the graphs.

3. Algebraically, the solutions are at :











or

or