Question

Plot a graph for the equation $y=-x^2+4x-1$.

Answer 1

$a=-1,b=4,c=-1$. As $a$ is negative, the parabola should open down.
Vertex: $x=-b/2a=2$. Putting this value of $x$, we get $y=3$.
Hence, the vertex of the parabola is $(2,3)$.
Assume two values of $x$ as follows and find the corresponding values of $y$.

$x$	$1$	$-1$
$y$	$2$	$-6$

Points obtained are $(1,2)$ and $(-1,-6)$.
Points obtained are $(2,3)$ (vertex), $[1,2]$, and $[-1,-6]$.
Symmetry of parabola: Mirror image points of $(1,2)$ and $(-1,-6)$ are $(3,2)$ and $(5,-6)$, respectively.
Now, sketch the parabola as shown in Fig.