3a. Convert the following function in standard form to vertex form by
completing the square
y = x^2+ 8x +17
1 Add file

y = (x + 4)² + 1

Step-by-step explanation:

Given

y = x² + 8x + 17

To complete the square

add/subtract ( half the coefficient of the x- term )² to x² + 8x

y = x² + 2(4)x + 16 - 16 + 17

  = (x + 4)² + 1 ← in vertex form

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15