Question

Identify the maximum value of the quadratic function given by the equation f(x)=-x^2+4x-1

Answer 1

`f(x)=ax^2+bx+c\\\\f(x)=-x^2+4x-1\\\\a=-1,\ b=4,\ c=-1\\\\a < 0\ \text{then the parabola ope}\text{n down,}\\\text{ terefore the maximum value is in vertex}.\\\\\text{The formula of a vertex}\\\\(h,\ k),\ \text{where}\ h=(-b)/(2a),\ k=f(h)=(-(b^2-4ac))/(4a)`

`h=(-4)/(2(-1))=(-4)/(-2)=2\\\\k=f(2)=-2^2+4(2)-1=-4+8-1=3`

`\text{Answer: the maximum value is euqal 3 for x = 2}`