Answer
Axis of symmetry: x= -2.5
Vertex: (-2.5, 12.5)
The graph is shown below:
Work Step by Step
$y = -2x^{2} - 10x$
The standard form for a quadratic equation is
$y = ax^{2} + bx + c$ So a= -2, b= -10, and c= 0
Axis of symmetry:
The formula for axis of symmetry is
$x= \frac{-b}{2a}$
$x= \frac{-(-10)}{2(-2)}$
$x= \frac{10}{-4}$
x= -2.5
Vertex:
Plug in the x value of the axis of symmetry to find the y value of the vertex.
$y = -2x^{2} - 10x$
$y = -2(-2.5)^{2} - 10(-2.5)$
y= 12.5
The vertex is (-2.5, 12.5)
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 and then graphing it downwards.
