Answer:
y = 6(x -(-3/2))^2 - 13/12
Step-by-step explanation:
Given: [tex]6x^2 +18x + 14[/tex]
We have to write in vertex form y = a(x -h)^2 + k
Step 1: In the given function y = 6x^2 + 18x + 14, the coefficient of x^2 is 6, we need to make it 1, so we take out 6 and factor it.
y = 6(x^2 + 3x + 7/6)
x^2 + 3x + 7/6, the value of b = 3, now divided 3 by 2, then square it.
(3/2)^2 = 9/4
Now add and subtract 9/4
y = 6(x^2 + 3x +9/4 -9/4 + 7/6)
y = 6(x +3/2)^2 -9/4+ 7/6
y = 6(x -(-3/2))^2 + [tex](\frac{-27 + 14}{24} )[/tex]
Here we simplified -9/4 + 7/6 taking the LCD as 12
[tex]y = 6(x - (-\frac{3}{2}))^2 +(\frac{-13}{12} )[/tex].
This can be written as
[tex]y = 6(x -(-\frac{3}{2} )^2 -\frac{13}{12}[/tex]
