Question

The function g(n) = n2 − 20n + 95 represents a parabola.

Answer 1

$n^2 - 20n + 95=\\ n^2-20n+100-5=\\ (n-10)^2-5$

Vertex - $(10,-5)$
It's a minimum, because $a\ \textgreater \ 0$

The axis of symetry is x=h where h is the x-coordinate of the vertex.
So it's $x=10$

Answer 2

Answer:

$g(n)=(n-10)^2-5$

The vertex will be at $(10, -5)$

$x=10$

Step-by-step explanation:

The given quadratic function is,

$g(n) = n^2-20n+95$

$=n^2-2\cdot n\cdot 10+95$

$=(n^2-2\cdot n\cdot 10+10^2)-10^2+95$

$=(n-10)^2-100+95$

$=(n-10)^2-5$

The vertex form is,

$g(n)=(n-10)^2-5$

The vertex will be at $(10, -5)$

As the leading coefficient of $g(n) = n^2-20n+95$ is positive, so the parabola will open upwards. Hence, at the vertex the value will be minimum.

The axis of symmetry will be,

$x=-\dfrac{b}{2a}$

Putting the values,

$x=-\dfrac{-20}{2\times 1}=10$