Question

What are the coordinates of the vertex f(x)=2(x+1)(x+3)

Answer 1

Answer:

$(-2,-2)$

Step-by-step explanation:

There are many methods to find the vertex of a quadratic function. The method that I will show you is by using the roots of the function

In the case of this function, the roots are $x=-1, x=-3$..

The vertex of a function will always be directly between these roots. The number that is directly between -1 and -3 is -2. This means that the x-value of our vertex is -2.

Now that we have the x-value, we can plug this into the function in order to get our y-value.

$2(x+1)(x+3)\\\\2(-2+1)(-2+3)\\\\2(-1)(1)\\\\-2$

We have found that our y-value is -2. This means that the coordinates of the vertex are $(-2,-2)$