SOLUTION: Find the exact vertex of the parabola algebraically... f(x) = -3x^2 + 5x + 1

Question 192072: Find the exact vertex of the parabola algebraically...
f(x) = -3x^2 + 5x + 1

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
f(x) = -3x^2 + 5x + 1
---
Use completing the square:
3x^2 -5x + ? = -y + 1 + ?
3(x^2 - (5/3)x + (5/6)^2) = -y + 1 +3(5/6)^2
---
3(x-(5/3))^2 = -y + 1 + (25/12)
3(x-(5/3))^2 = -y + (37/12)
3(x-(5/3))^2 = -(y - (37/12)
(x-(5/3))^2 = (-1/3)(y-(37/12))
Vertex: (5/3 , 37/12)
============================
Graph:

===========================
Cheers,
Stan H.

RELATED QUESTIONS
Find the exact vertex of the parabola algebraically... f(x) = -3x^2 + 5x + 1... (answered by nerdybill)

Find the exact vertex of the parabola algebraically... f(x) = (x - 1)^2 + (x + 3) (answered by nerdybill)

I need to find the vertex of the parabola... (answered by JessicaGill)

Find the vertex of the parabola:... (answered by drk)

Find the vertex of the parabola.... (answered by lwsshak3)

find the vertex of the parabola f(x)=... (answered by lwsshak3)

Please help me with these three problems. Solve each equation by using the quadratic... (answered by jessicaherndon)

Find the x-coordinate of the vertex of the parabola defined by the function f(x)=... (answered by josgarithmetic,MathTherapy)

f(x)=5x^2+20x+30 Express in standard form Find the Vertex Graph the parabola (answered by lwsshak3)