Question

How do you identify the important parts of `f(x)=-x^2+4x-6` to graph it?

Answer 1

Graph `f(x) = -x^2 + 4x - 6`

Explanation:

The important parts are:
a. x-coordinate of axis of symmetry:
`x = (-b/(2a)) = -4/-2 = 2`
b x-coordinate of vertex: same as the one of axis of symmetry:
x = 2
y-coordinate of vertex:
y = f(2) = -4 + 8 - 6 = -2.
c. y-intersect. Make x = 0 --> y = -6.
d. x- intercepts. make y = 0 --> Solve: `- x^2 + 4x - 6 = 0.`
`D = b^2 - 4ac = 16 - 24 = - 8`. There are no real roots (No x-intercepts). The parabola open downward (a < 0) and it is completely below the x-axis.
graph{-x^2 + 4x - 6 [-10, 10, -5, 5]}