find the vertex and the axis of symmetry andf(x)=x^2-10x+21`

Question

graph the function

Answer 1

there are many ways to solve for the vertex. i think the easiest is to first find the derivative and solve for x:
f(x)=x^2-10x+21
f'(x) = 0 = 2x - 10
2x = 10
x = 5
now substitute this back to original:
f(5) = 5^2 - 10*5 + 21
f(5) = 25 - 50 + 21
f(5) = -4
thus vertex is at (5, -4).
and axis of symmetry is x = 5.

hope this helps~ :)