# How do you find the vertex of a parabola #y = -2(x+1)(x-5)#?

##### 1 Answer

The vertex is at the point

#### Explanation:

Consider a parabola represented by a quadratic polynomial

If

If

In both cases the X-coordinate of a vertex is

Parabola is a symmetrical figure, its vertical axis of symmetry intersects the X-axis in exactly the same point where it reaches its minimum (for

If we are dealing with a quadratic polynomial that can be equal to zero at some values of

has solutions

the central point

Therefore, in case we have two solutions mentioned above, all we have to do to find a vertex is

(a) find these two solutions

(b) find a midpoint between them:

The given problem presents an easy case, when the solutions to an equation

Hence, the midpoint between them is

So, we have determined that X-coordinate of the parabola's axis of symmetry as

The Y-coordinate is

So the vertex is at point