The discussion revolves around the quadratic expression -x^2 + 4x, focusing on completing the square and finding the vertex of the parabola represented by the equation. Participants are examining the implications of the negative coefficient in front of the x^2 term and its effect on the vertex calculation.
Multiple interpretations of the steps to complete the square are being explored, with some participants providing guidance on balancing the equation after adding terms inside the parentheses. There is an ongoing examination of the vertex location, with no explicit consensus reached yet.
Participants are grappling with the implications of the negative leading coefficient and how it influences the vertex position. The discussion is framed within the constraints of homework expectations, emphasizing understanding rather than providing direct solutions.
The error is here. You have actually added -4 inside the parentheses to complete the square, so to keep the expression equal, you need to add + 4.Miike012 said:Problem: -x^2 + 4x
- ( x^2 - 4x + (4/2)^2 ) - 4
Miike012 said:= - (x - 2) - 4
Vertex is at (2, -4)
but the vertex is obviously at (2,4)...
what did I do wrong.
Mark44 said:Let's go through the steps.
-x2 + 4x
= -(x2 - 4x)
= -(x2 - 4x + 4) + 4
I put in +4 inside the parentheses, but due to the minus sign out front, I have actually added -4, so to balance, I have to add + 4.
= -(x - 2)2 + 4