Question

What is the axis of symmetry and vertex for the graph `y = 6x^2 - 11x - 10`?

Answer 1

The formula for the axis of symmetry is given as `x = -b/(2a)`
in the quadratic equation

In this equation, the b value is -11 and the a value is 6

Thus, the axis of symmetry is `x = 11 / 12`

Now we found the horizontal line, we must find the place where this horizontal like meets the equation because that is where the vertex is.

Well, to find that, we just plug in `x = 11/12` into the given equation

`y = 6(11/12)^2 - 11(11/12) - 10`

`y = 6(121/144) - (121/12) - 10`

Changing the denominator so that all parts have the same one

`y = 121/24 - 242/24 - 240/24`

`y = -361/24`

So, our vertex is `(11/12, -361/24)`