SOLUTION: write the equation of the axis of symetry and find the coodinates. identify the vetext as a maximum or miumum y=3x^2-6x-4

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Question 47865: write the equation of the axis of symetry and find the coodinates. identify the vetext as a maximum or miumum

y=3x^2-6x-4
Found 2 solutions by Nate, stanbon:
Answer by Nate(3500) (Show Source):
You can put this solution on YOUR website!
y = 3x^2 - 6x - 4
v(-b/2a,f(x))
Since the parabola is vertical, the Axis of Symmetry is:

Since the value of is positive, the parabola opens upwards. The vertex is a minimum.

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
write the equation of the axis of symetry and find the coodinates. identify the vetext as a maximum or miumum

y=3x^2-6x-4
Put this in the form (x-h)^2 = 4p(y-k) by completing the square, as follows:
y+4+3=3(x^2-2x+1)
y+7=3(x-1)^2
(x-1)^2=(1/3)(y+7)
Axis of symmetry: x=1
Vertex (1,-7) is a minimum

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=84 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 2.52752523165195, -0.527525231651947. Here's your graph:

Cheers,
Stan H.