What Is The General Form Of y = (x+6)²+1?

Question

pls help me im having a hard time in this topic lmao

Answer 1

y = (x + 6)² + 1

Standard form is y = ax² + bx + c

1. Expand or multiply out (x + 6)², remember (x + 6)² is (x + 6)(x + 6) which is x*x + x*6 + 6*x + 6*6
2. Written in the standard way that becomes x² + 6x + 6x + 36.
3. Combine the like terms 6x and 6x now you have x² + 12x + 36. So, (x + 6)² is x² + 12x + 36
4. Replacing (x + 6)² in the original equation with the equivalent expression, x² + 12x + 36, and you have y = x² + 12x + 36 + 1
5. Combine the like terms 36 and 1 and you get y = x² + 12x + 37, which is standard form