Answer: (2, -25)
Step-by-step explanation:
Let's find the roots aka x intercepts.
Plug in y = 0 and solve for x.
y=(x+3)(x-7)
(x+3)(x-7) = 0
x+3 = 0 or x-7 = 0
x = -3 or x = 7 are the two roots.
Now find the midpoint of those roots.
Add them up and divide in half.
(-3+7)/2 = 4/2 = 2
The midpoint happens at x = 2, which is the x coordinate of the vertex. This is the axis of symmetry where the vertex is located.
The vertex in this case is the lowest point on the parabola. It's the turning point where it goes from decreasing to increasing.
Plug x = 2 back into the original equation to find its paired y value.
y=(x+3)(x-7)
y=(2+3)(2-7)
y=(5)(-5)
y=-25
Therefore, the vertex is located at (2, -25) as indicated in the graph below. I used GeoGebra to make the graph. Desmos is another good choice.