Question

Find b and c so that y=-7x^2+bx+c has vertex (4,9). Can someone show me step by step? I got b=56 and c=-103

Answer 1

hmm ... if we can turn this into the vertex form id be simpler i think

Answer 2

y = -7x^2 + bx + c ; lets start by factoring out that -7 from
the first 2 terms

y = -7(x^2 - bx/7) + c ; how we can complete the square to change
its form

y = -7(x^2 - bx/7 + (2b/7)^2) + 7(2b/7)^2 + c

now we can compact it ... maybe

y = -7(x^2 - 2b/7)^2 + 7(2b/7)^2 + c

this is the vertex form if i did it right

Answer 3

i got my divide by 2 off; spose to be b/14, not 2b/7

Answer 4

y = -7(x^2 - b/14)^2 + 7(b/14)^2 + c

thats better, hopefully

Answer 5

now, the vertex is:

(b/14 , 7(b/14)^2 + c) which needs to equate to (4,9)

b/14 = 4

7(b/14)^2 + c = 9
-----------------------------

b/14 = 4

b = 56
.........................

7(b/14)^2 + c = 9

7(56/14)^2 + c = 9

c = 9 - 7(56/14)^2

Answer 6

so yeah, b=56 and c=-103 :)

Answer 7

thank you! i have been gone from my class on family emergency and have to learn this on my own. the book doesnt really help.

Answer 8

i got no idea what your book would tell you to do, i just took what i knew and tried to keep me head on stratight till i got to the end :)

Answer 9

haha yea!