Answer:
2.8 in
Step-by-step explanation:
Let's first solve for the quadratic equation
[tex]3x^2 - 12x + 6 =0[/tex]
Using the quadratic formula the roots of the quadratic equation
[tex]ax2 + bx + c = 0[/tex]
are
[tex]x_{1,2} = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{ 2a }[/tex]
In the specific equation for the given parabola we note
a = 3
b = -12
c = 6
Therefore the roots are:
[tex]x_{1, 2} = \dfrac{ -(-12) \pm \sqrt{(-12)^2 - 4(3)(6)}}{ 2(3) }\\\\x_{1, 2} = \dfrac{ 12 \pm \sqrt{144 - 72}}{ 6 }\\\\x_{1, 2} = \dfrac{ 12 \pm \sqrt{72}}{ 6 }\\\\x_{1, 2} = 2 \pm \sqrt{2}\\\\x_{1, 2} = 0.585786, \;\;3.41421[/tex]
These are the zeros of the graph i.e. the points where where graph intersects the x-axis
These points correspond to the left and right x-coordinates of the vase opening
The width is the difference between the two
= 3.41421 - 0.585786
= 2.828424
Rounding to the nearest tenth we get the width as 2.8 in
