Answer
Axis of symmetry: x= 1.5
Vertex: (1.5, -3.5)
The graph is shown below:
Work Step by Step
$y = 2x^{2} - 6x + 1$
The standard form for a quadratic equation is
$y = ax^{2} + bx + c$ So a= 2, b= -6, and c= 1
Axis of symmetry:
The formula for axis of symmetry is
$x= \frac{-b}{2a}$
$x= \frac{-(-6)}{2(2)}$
$x= \frac{6}{4}$
x= 1.5
Vertex:
Plug in the x value of the axis of symmetry to find the y value of the vertex.
$y = 2x^{2} - 6x + 1$
$y = 2(1.5)^{2} - 6(1.5) + 1$
y= -3.5
The vertex is (1.5, -3.5)
We plot the vertex on the graph. Since the a value is 2 and is positive the parabola opens upwards. So we graph a parabola starting from the vertex and then graphing it upwards.
