Rewrite the equation in term of x and y.
Complete the square for 2x² - 8x + 5
Use the form ax² + bx + c, to find the values of a, b, and c.
a = 2, b = -8, c = 5
Consider the vertex form of a parabola.
a(x+d)² + e
Substitute the values of a and b into the formula d = b/2a
d = -8/2(2)
simplify the right side
cancel the common factor of 8 and 2
factor 2 out of 8
d = -2 · 4/ 2 · 2
cancel the common factors
factor 2 out of 2 · 2
d = -2·4/2(2)
cancel the common factor
d = -2 · 4/2 · 1
rewrite the expression
d = -4/2
Cancel the common factor of 4 and
2 .
factor 2 out of 4
d = -2· 2 / 2
cancel the common factors.
factor 2 out of 2
d = -2·2/2(1)
cancel the common factor
d = -2·2/2 · 1
rewrite the expression
d = -2/1
divide 2 by 1
d = -1 * 2
multiply -1 by 2
d = -2
find the value of e using the formula e = c-b2/4a
simplify each term
raise -8 to the power of 2
e = 5 - 64 / 4 * 2
multiply 4 by 2
e = 5 - 64/8
divide 64 by 8
e = 5-1 · 8
multiply -1 by 8
e = 5-8
subtract 8 from 5
e = -3
substitute the values of a,d , and e into the vertex form a (x+d)² + e
2(x-2)²-3
set y equals to the new right side
y =2 (x-2)²-3
use the vertex form, y = a (x-h)² + k, to determine the values of a,h, and k
a = 2
h = 2
k = -3
find the vertex (h,k).
(2,-3)