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]}
