Answer
See the graph
Work Step by Step
$f(x)=-x^2+4x+3$
Find the axis of symmetry and the coordinates of the vertex.
$x=\frac{-b}{2a}=\frac{-4}{2.(-1)}=2$
The axis of symmetry is $x=2$. So the x-coordinate of the vertex is $2$.
Substitute 1 for x to find the y-coordinate of the vertex.
$y=-(2)^2+4(2)+3$
$=17$
The vertex is $(2,17)$
Find some other points for the graph.
$(0,3)$
$(1,6)$
$(3,6)$
$(4,3)$
Graph the vertex and the points we found.
