Question

How do you graph `f(x) = -x^2 + 2x - 4`?

Answer 1

Refer explanation section.

Explanation:

Given -
y = `-x^2 + 2x -4`

It is a U shaped curve. Since the sign of the `x^2` is negative, it is concave downwards.

Find the vertex -

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

It means when x takes the value 1, the curve turns.
Take a few values on either side of 1. Calculate corresponding y values. Plot the pairs. Join them with the help of a smooth curve

x : y
-2 : -12
-1 : -7
0 : -4
1 : -3
2 : -4
3 : -7
4 : -12
graph{-x^2 +2x -4 [-11.79, 8.21, -8.76, 1.24]}