y=4x^2-5x-1y=4x2−5x−1 is a quadratic formula in standard form:
ax^2+bx+cax2+bx+c,
where:
a=4a=4, b=-5b=−5, and c=-1c=−1
The vertex form of a quadratic equation is:
y=a(x-h)^2+ky=a(x−h)2+k,
where:
hh is the axis of symmetry and (h,k)(h,k) is the vertex.
The line x=hx=h is the axis of symmetry. Calculate (h)(h) according to the following formula, using values from the standard form:
h=(-b)/(2a)h=−b2a
h=(-(-5))/(2*4)h=−(−5)2⋅4
h=5/8h=58
Substitute kk for yy, and insert the value of hh for xx in the standard form.
k=4(5/8)^2-5(5/8)-1k=4(58)2−5(58)−1
Simplify.
k=4(25/64)-25/8-1k=4(2564)−258−1
Simplify.
k=100/64-25/8-1k=10064−258−1
Multiply -25/8−258 and -1−1 by an equivalent fraction that will make their denominators 6464.
k=100/64-25/8(8/8)-1xx64/64k=10064−258(88)−1×6464
k=100/64-200/64-64/64k=10064−20064−6464
Combine the numerators over the denominator.
k=(100-200-64)/64k=100−200−6464
k=-164/64k=−16464
Reduce the fraction by dividing the numerator and denominator by 44.
k=(-164-:4)/(64-:)k=−164÷464÷
k=-41/16k=−4116
Summary
h=5/8h=58
k=-41/16k=−4116
Vertex Form
y=4(x-5/8)^2-41/16y=4(x−58)2−4116
graph{y=4x^2-5x-1 [-10, 10, -5, 5]}
