Question

How do i find the vertex,axis of symmetry,min/max value?

a) x^2-9x+y+20

b) f(x)=-5/4x^2+5/28x-5/114

c) f(x)=5x^2+x+4

Answer 1

complete the square
I will do the last one

y = 5 x^2 + x + 4
need 1 as coef of x^2 so divide by 5
y/5 = x^2 + (1/5) x + 4/5
subtract 4/5 from both sides
y/5 - 4/5 = x^2 + (1/5)x
half of 1/5 is 1/10, square it and add to both sides
Y/5 -80/100 + 1/100 = x^2 + (1/5) x + 1/100
y/5 - 79/100 = (x + 1/10)^2
symmetric about x = -1/10
so vertex and min/max is on x = -1/10
then
y/5 = 79/100
y = 79/20
so vertex at (-1/10 , 79/20)
is that a max or a min ?
as x gets big, y gets big so the vertex is a min

By the way your first one, a), is a typo. (no = sign)