Standard form into Vertex form

Question

Put the function y = 7 x^2 + 14 x + 18 in vertex form f(x) = a(x-h)^2 + k and determine the values of a, h, and k.

Answer 1

Dear Emilee,

    Here is a different method to work the problem.

 

Question:  Change y=7X²+14X +18  to vertex form, which is f(X)=a(X-h)² + k.  Vertex point(h,k).

                Determine "h, k," and "a."

 

 

Use the formula:  h=-b/2a, where k=f(h).                      Standard form of quadratic:  aX² +bX +C =y=0

 

 

y=7X²+14X +18         Determine  "a," and " b."       a=7  and b=14

 

 

h=- (b)/2a    =   -(14)/2(7)    =-14/14  = -1       Substitution     h= -1

 

 

f(-1)=  7(-1)² + 14(-1) + 18 =    7+ -14 +18= -7 +18 = 11=K      

 

                                

                                          (h,k)=(-1, 11)     a=7,  b=14, h= -1, k=11        Answer

 

f(X)=7(X-(-1)² + 11.                        f(X)=7(X+1)² + 11.                             Answer

 

 

 

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                                                                        Susan C.

 

 

 

 

Answer 2

y = 7x² + 14x + 18                 Use completion of the square, leave room

y = 7x² + 14x         + 18         Factor out the 7

y = 7(x² + 2x        ) + 18         Determine the new constant term

y = 7(x² + 2x + 1) + 18 - 7     The 1 added is multiplied by the 7.

y = 7(x + 1)² + 11

Answer 3

y = 7x² + 14x + 18

 

y = 7(x² + 2x) + 18

 

y = 7(x² + 2x + 1 - 1) + 18

 

y = 7(x² + 2x + 1) - 7 + 18

 

y = 7(x+1)² + 11

 

y = 7[x - (-1)]² + 11

 

a = 7    h = -1   k = 11

 

Vertex = (h, k) = (-1, 11)  

 

Since a = 7 > 0, the graph of the parabola opens upward with lowest point (-1, 11)).