Answer
Axis of symmetry: x=2
Vertex: (2, 17)
The graph is shown below:
Work Step by Step
$y = -2x^{2} + 8x + 9$
The standard form for a quadratic equation is
$y = ax^{2} + bx + c$ So a= -2, b= 8, and c= 9
Axis of symmetry:
The formula for axis of symmetry is
$x= \frac{-b}{2a}$
$x= \frac{-(8)}{2(-2)}$
$x= \frac{-8}{-4}$
x=2
Vertex:
Plug in the x value of the axis of symmetry to find the y value of the vertex.
$y = -2x^{2} + 8x + 9$
$y = -2(2)^{2} + 8(2) + 9$
y= -8 + 16 + 9
y= 17
The vertex is (2, 17)
We plot the vertex on the graph. Since the a value is -2 and is negative the parabola opens downwards. So we graph a parabola starting from the vertex opening downwards.
