Find b and c so that y = 1 x 2 + b x + c has vertex ( 2 , − 6 ) .

Question

math answer the question please

 

Answer 1

For y = Ax²+Bx+C, the x-coordinate of the vertex is -B/(2A).

 

So, for y = x²+bx+c, since the vertex is (2,-6), we have -b/(2(1)) = 2.

 

                                                                                          b = -4

 

Thus, y = x² - 4x + c

 

Since the vertex is a point on the graph, we have -6 = 2² - 4(2) + c

 

                                                                        -6 = -4 + c

 

                                                                         c = -2

 

So, y = x² - 4x - 2

 

Answer 2

f(x) = x² + bx + c

 

The coordinate of the vertex of the parabola is:

(-b/2a, f(-b/2a))

 

Since the vertex is at (2, -6) then:

 

-b/2a = 2

-b/2(1) = 2

-b = 4

b = -4

 

So far the equation is:  y = x² - 4x + c

 

AND

 

f(2) = -6

-6 = 2² -4(2) + c

-6 = 4-8+c

-6 = -4+c

-2 = c

 

Your parabola is:  f(x) = x² - 4x - 2

Or, if you prefer:  y = x² - 4x - 2

 

Check:  -b/2a = 4/2 = 2

 

f(2) = 2² -4(2)  - 2 = 4-10 = -6

 

vertex: (2, -6)

 

Note:   There are other ways to work this problem as I'm sure someone will post.  :-)