Question

The function f is given by f(x) = (x + 3)^2 - 1.

1) Write the coordinates of the vertex of the graph of f.
2) Does the graph open up or down? How do you know?

Answer 1

the coordinate of the vertex is going to be (-3,-1) and it's concave up

Explanation:

1.notice this function is in graphing form (x-h)^2+k, where (h,k) is your coordinate of the vertex, hence in this problem it's going to be (-3,-1)

2. notice that this function have a parent function of x^2, where it's a parabola that is concave up which in this case is basiclly the same shape it's also concave up

In calculus, we can proof it by finding the first derivatives and find the critical points, then take the second derivative at that critical points to see if that's negative or positive in this case it's positive