put in vertex form and determine vertex

Question

write the quadratic function the form f(x)=a(x-h)^2+k
then, give the vertex of its graph

quadratic function given: f(x)=3x^2+30x+74

Answer 1

• From the given function f(x) = 3x^2+30x+74, a=3, b=30, c=74.
• Use the Vertex Formula to solve this problem.
• (-b/(2a)) , f(-b/(2a))
• -b/(2a) = -(30)/(2*3) = -5 = h.
• f(-b/(2a)) = 3(-5)^2 + 30(-5) + 74
•                    75 +-150 +74 = -1 = k.
• VERTEX = (h,k) = (-5,-1).
• f(x)=a(x-h)^2+k in the form of the solution is y = 3(x+5)^2 -1.

Answer 2

The quadratic function given is:

 

f(x) = 3x² + 30X + 74

 

In order to rewrite the function in vertex form, we need to rewrite the function by completing the square

 

f(x) = 3(x² + 10x + ? ) + 74

 

Completing the square for x² + 10x +25 equals (x+5)² 

 

Since we added 3*25 or 75 to the right side of the equation, we need to subtract 75 to balance the equation.

 

f(x) = 3(x+5)² + 74 -75

 

f(x) = 3(x+5)2 -1

 

The vertex is located at (-h, k)

 

h = -5 and k = -1

 

Answer 3

f(x)=3x^2+30x+74

y=3x^2+30x+74

y-74=3x^2+30x

y-74=3(x^2+10x)

y-74+3[  ]=3(x^2+10x)

complete the square

y-74+3[25]=3(x^2+10x+25)

y-74+75=3(x+5)^2

y+1=3(x+5)^2

y=3(x+5)^2-1

y=3(x-[-5])^2-1

vertex: (-5,-1)

 

short-cut...

h=-b/2a and k=f(h)

h=-30/6

h=-5

k=3(25)+30(-5)+74

k=75-150+74

k=-1

(-5,-1) again

Answer 4

f(x) = 3(x²+10x)+74

 

      = 3(x²+10x+25)-75+74

 

      = 3(x+5)²-1

 

Vertex = (-5, -1)