SOLUTION: Find the vertex of the graph of f(x)= 3x^2-12x+5 and determine whether the graph opens up or down is there a formula to figure this out. please help and thank you

Question 1129793: Find the vertex of the graph of f(x)= 3x^2-12x+5 and determine whether the graph opens up or down

is there a formula to figure this out. please help and thank you
Found 3 solutions by stanbon, MathLover1, MathTherapy:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
Find the vertex of the graph of f(x)= 3x^2-12x+5 and determine whether the graph opens up or down
is there a formula to figure this out. please help and thank you
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The form is y = ax^2+bx+c
a = 3 ; b = -12 ; c = 5
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If a is positive the graph opens up
If a is negative the graph opens down
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Where is the vertex ?
The roots are -b/(2a)-sqrt(b^2-4ac) and -b/(2a)+sqrt(b^2-4ac)
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Notice that -b/(2a) is midway between those roots.
i.e. if the roots are at x = 2 and x = 6, -b/(2a) will be 4
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The vertex always splits the quadratic into two symmetric wings.
So the vertex must pass thru -b/2a.
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If the quadratic goes up or down the vertex is at (-b/(2a),f(-b/(2a))
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Your problem:: The vertex is at (12/6,f(2))
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Cheers,
Stan H.
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Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

When you have a quadratic function in either form, OR , if , then the parabola opens , if , then the parabola opens .
The vertex is the or (depending on direction) on the graph of a quadratic function.

-> -> and the parabola opens
to find the vertex of the graph, write your equation in vertex form
The vertex formula is derived from the completing-the-square

=> the vertex (,) is (,)

Answer by MathTherapy(10555)   (Show Source): You can put this solution on YOUR website!
Find the vertex of the graph of f(x)= 3x^2-12x+5 and determine whether the graph opens up or down

is there a formula to figure this out. please help and thank you

Standard form of a quadratic function:
In this case, a = 3; b = - 12; c = 5
The formula for the x-coordinate or axis of symmetry is:
----- Substituting - 12 for b, and 3 for a
------- Substituting 2 for x

Since a = 3, a > 0, or is POSITIVE so the graph opens UPWARD.
IGNORE that woman's answer as she posted a WRONG vertex!!
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