Question

How do you identify the important parts of `f(x)= x^2 - 10x + 5` to graph it?

Answer 1

The point at which curve turns is the most important part of a graph.

Explanation:

Let `y=x^2−10x+5`

The important part of the graph is where the curve turns.
Quadratic functions normally have only one turn.
Either, it will decrease,turn and then increase or it will increase, turn and then decrease.

Since coefficient of `x^2` is positive the curve is upward facing 'U' shaped curve.

The vertex gives you where the curve turns.

`x=(-b)/(2a) =-(-10)/(2 xx 1)=10/2 = 5`

At `x=5 -> y = 5^2-(10 xx 5)+5=-20`

At `(5,-20)` the curve turns. When you obtain the curve it must find a place.

Now take a few points on either side of `5`. Find their respective `y` values. Plot them. Join all the points with a smooth curve.

x: y
2: -11
3: -16
4: -19
5: -20
6: -19
7: -16
8: -11

graph{x^2-10x+5 [-58.5, 58.53, -29.27, 29.26]}