Question

Need again vertex,line of symmetry,max/min value of f(x)-x^2+10x+4

Answer 1

Well, wherever the vertex is will be the max/min depending on if the parabola is rightside up or upside down. The line of symmetry will be the x value of the vertex. To find the vertex, complete the square:
\[f(x)=x^2+10x+25-25+4=(x+5)^2-21\]
So your vertex is at:(-5,-21)
Which means your line of symmetry is x=-5
And means that your minimum is at -21 (since you can see there is a y-intercept at 4 from the original equation so it must be ABOVE -21; i.e., -21 is the minimum)
http://www.wolframalpha.com/input/?i=minimize+x^2%2B10x%2B4

Answer 2

f(x)=(x+5)^2-21
vertex is (-5,-21)
y'=0=2x+10
x=-5
y''=2>0 is minimum point

Answer 3

f(x)=(x+5)^2-21
vertex is (-5,-21)
y'=0=2x+10
x=-5
y''=2>0 is minimum point

Answer 4

thanks