### 2 Answers

- King LeoLv 74 months ago
v(t) = t² + 11t - 4

v(t) = ( t + 11/2 )² - ( 11/2 )² - 4

v(t) = ( t + 11/2 )² - 137/4

vertex = ( -11/2, -137/4 )

━━━━━━━━━━━

line of symmetry at vertex

t = -11/2

━━━━

- llafferLv 74 months ago
If you put this into vertex form:

v(t) = a(t - h)² + k

The vertex is the point (h, k)

And the axis of symmetry would be t = h

So to get your equation into vertex form:

v(t) = t² + 11t - 4

Let's get the right side into the form of (t² + bt) by adding 4 to both sides:

v(t) + 4 = t² + 11t

Now complete the square by adding 121/4 to both sides:

v(t) + 4 + 121/4 = t² + 11t + 121/4

Now we can simplify the left side and factor the right:

v(t) + 16/4 + 121/4 = (t + 11/2)²

v(t) + 137/4 = (t + 11/2)²

Finally, solve for v(t) again:

v(t) = (t + 11/2)² - 137/4

The vertex is the point (-11/2, -137/4)

And the axis of symmetry is t = -11/2