#y=4x^2-5x-1# is a quadratic formula in standard form:

#ax^2+bx+c#,

where:

#a=4#, #b=-5#, and #c=-1#

The vertex form of a quadratic equation is:

#y=a(x-h)^2+k#,

where:

#h# is the axis of symmetry and #(h,k)# is the vertex.

The line #x=h# is the axis of symmetry. Calculate #(h)# according to the following formula, using values from the standard form:

#h=(-b)/(2a)#

#h=(-(-5))/(2*4)#

#h=5/8#

Substitute #k# for #y#, and insert the value of #h# for #x# in the standard form.

#k=4(5/8)^2-5(5/8)-1#

Simplify.

#k=4(25/64)-25/8-1#

Simplify.

#k=100/64-25/8-1#

Multiply #-25/8# and #-1# by an equivalent fraction that will make their denominators #64#.

#k=100/64-25/8(8/8)-1xx64/64#

#k=100/64-200/64-64/64#

Combine the numerators over the denominator.

#k=(100-200-64)/64#

#k=-164/64#

Reduce the fraction by dividing the numerator and denominator by #4#.

#k=(-164-:4)/(64-:)#

#k=-41/16#

**Summary**

#h=5/8#

#k=-41/16#

**Vertex Form**

#y=4(x-5/8)^2-41/16#

graph{y=4x^2-5x-1 [-10, 10, -5, 5]}