Question

Find the vertex of the graph of f(x) = x2 + 4x - 5.

Answer 1

You can solve this in two ways.

1. Graphical. Plot the graph for x between -5 and 1 (see attachement).
The vertex of the graph is the peak of the curve, which has the coordinates x=-2, y=-9.

2. Analytical. Calculate the derivative of the function f(x)
$\frac{df}{dx}=2x+4$
Solve the equation:
$2x+4=0$
will give the solution x=-2.
Replace x=-2 in the f(x) function and you'll get the value of y:
$(-2)^2+4 \cdot (-2)-5=4-8-5=-9$

You get the same answer: x=-2, y=-9

So the answer is
B. (-2, -9)