Algebra Examples
y=x2-8x-4y=x2−8x−4
Step 1
Step 1.1
Complete the square for x2-8x-4x2−8x−4.
Step 1.1.1
Use the form ax2+bx+cax2+bx+c, to find the values of aa, bb, and cc.
a=1a=1
b=-8b=−8
c=-4c=−4
Step 1.1.2
Consider the vertex form of a parabola.
a(x+d)2+ea(x+d)2+e
Step 1.1.3
Find the value of dd using the formula d=b2ad=b2a.
Step 1.1.3.1
Substitute the values of aa and bb into the formula d=b2ad=b2a.
d=-82⋅1d=−82⋅1
Step 1.1.3.2
Cancel the common factor of -8−8 and 22.
Step 1.1.3.2.1
Factor 22 out of -8−8.
d=2⋅-42⋅1d=2⋅−42⋅1
Step 1.1.3.2.2
Cancel the common factors.
Step 1.1.3.2.2.1
Factor 22 out of 2⋅12⋅1.
d=2⋅-42(1)d=2⋅−42(1)
Step 1.1.3.2.2.2
Cancel the common factor.
d=2⋅-42⋅1d=2⋅−42⋅1
Step 1.1.3.2.2.3
Rewrite the expression.
d=-41d=−41
Step 1.1.3.2.2.4
Divide -4−4 by 11.
d=-4d=−4
d=-4d=−4
d=-4d=−4
d=-4d=−4
Step 1.1.4
Find the value of ee using the formula e=c-b24ae=c−b24a.
Step 1.1.4.1
Substitute the values of cc, bb and aa into the formula e=c-b24ae=c−b24a.
e=-4-(-8)24⋅1e=−4−(−8)24⋅1
Step 1.1.4.2
Simplify the right side.
Step 1.1.4.2.1
Simplify each term.
Step 1.1.4.2.1.1
Raise -8−8 to the power of 22.
e=-4-644⋅1e=−4−644⋅1
Step 1.1.4.2.1.2
Multiply 44 by 11.
e=-4-644e=−4−644
Step 1.1.4.2.1.3
Divide 6464 by 44.
e=-4-1⋅16e=−4−1⋅16
Step 1.1.4.2.1.4
Multiply -1−1 by 1616.
e=-4-16e=−4−16
e=-4-16e=−4−16
Step 1.1.4.2.2
Subtract 1616 from -4−4.
e=-20e=−20
e=-20e=−20
e=-20e=−20
Step 1.1.5
Substitute the values of aa, dd, and ee into the vertex form (x-4)2-20(x−4)2−20.
(x-4)2-20(x−4)2−20
(x-4)2-20(x−4)2−20
Step 1.2
Set yy equal to the new right side.
y=(x-4)2-20y=(x−4)2−20
y=(x-4)2-20y=(x−4)2−20
Step 2
Use the vertex form, y=a(x-h)2+ky=a(x−h)2+k, to determine the values of aa, hh, and kk.
a=1a=1
h=4h=4
k=-20k=−20
Step 3
Find the vertex (h,k)(h,k).
(4,-20)(4,−20)
Step 4
