Convert -16x^2 + 12x + 10 into vertex form

y = -16 (x − 3/8)² + 49/4

Step-by-step explanation:

y = -16x² + 12x + 10

First, factor the leading coefficient from the first two terms.

y = -16 (x² − 3/4 x) + 10

Complete the square.  Take half of the b coefficient, square it, then add and subtract the result.

b = -3/4

b/2 = -3/8

(b/2)² = 9/64

y = -16 (x² − 3/4 x + 9/64 − 9/64) + 10

y = -16 (x² − 3/4 x + 9/64) + 9/4 + 10

y = -16 (x − 3/8)² + 49/4

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)