Answer
Axis of symmetry: x=2
Vertex: (2,7)
The graph is shown below:
Work Step by Step
$y = -x^{2} + 4x + 3$
The standard form for a quadratic equation is
$y = ax^{2} + bx + c$ So a= -1, b= 4, and c= 3
Axis of symmetry:
The formula for axis of symmetry is
$x= \frac{-b}{2a}$
$x= \frac{-(4)}{2(-1)}$
$x= \frac{-4}{-2}$
x=2
Vertex:
Plug in the x value of the axis of symmetry to find the y value of the vertex.
$y = -x^{2} + 4x + 3$
$y = -(2)^{2} + 4(2) + 3$
y= -4 + 8 + 3
y= 7
The vertex is (2, 7)
We plot the vertex on the graph. Since the a value is -1 and is negative the parabola opens downwards. So we graph a parabola starting from the vertex and then graphing it downwards.
