Math final help?

f(x) = -11x² + 77x - 6 is a parabola so its line of symmetry runs through the vertex.

The x-coordinate of the vertex is x = -77/((2)(-11) = 77/22 = 3.5 so

the equation of the line of symmetry for f(x) is x = 3.5..............ANS

We can find the point of the vertex by putting this into vertex form:

y = a(x - h)² + k

So the vertex is the point (h, k)

The line of symmetry will be:

x = h

We get:

y = -11x² + 77x - 6

We need the right side to be in the form of (x² + bx) so we can complete the square, so add 6 to both sides and divide both sides by -11:

y + 6 = -11x² + 77x

-(y + 6) / 11 = x² - 7x

Now complete the square by adding 49/4 to both sides:

49/4 - (y + 6) / 11 = x² - 7x + 49/4

The right side now factors:

49/4 - (y + 6) / 11 = (x - 7/2)²

We can finish by solving for y, bye we have the info that we need:

The equation for the line of symmetry is:

x = 7/2

Rounded to the nearest tenth, we get:

x = 3.5

f (x) = -11x2 + 77x - 6

x axis of symmbetrt = -b/2a = -(77)/(2*-11) = 7/2