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Change the quadratic equation, f (x) = 2x2 – 8x + 5, into
vertex form.

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)

f(x) = 2(x-2)² - 3

Step-by-step explanation:

f(x) = 2x² - 8x + 5

a = 2

b = -8

c =

Subtract 5 from both sides

f(x) = 2x² - 8x + 5

- 5                   - 5

f(x) - 5 = 2x² - 8x

Add 8 to both sides

f(x) - 5 = 2x² - 8x

    + 8              + 8

f(x) + 3 = 2x² - 8x + 8

Factor the 2 out of the right side of the equation

f(x) + 3 = 2(x² - 4x + 4)

Factor the equation inside the parenthesis)

f(x) + 3 = 2(x - 2)(x - 2)

f(x) + 3 = 2(x - 2)²

Finally subtract the 3 from both sides

f(x) + 3 = 2(x - 2)²

      - 3            - 3

f(x) = 2(x - 2)² - 3

step-by-step explanation:

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cosine

step-by-step explanation: