Question

The vertex form of the equation of a parabola is y = (x + 3)2 + 53.
What is the standard form of the equation?

A. y = 6x2 + 9x+ 62
B. y = x2 + 6x + 62
C. y = x2 + 3x + 53
D. y = x2 + 53x + 42

Answer 1

@caozeyuan

Answer 2

can u explain pls

Answer 3

notice that the four choices have different linear terms

Answer 4

what do u mean by linear terms

Answer 5

do you want to do it the proper way or the easy way?

Answer 6

ik linear is straight but how do u know

Answer 7

y=ax^2=bx+c, bx is the linear term, since it is linear wrt x

Answer 8

oh ok

Answer 9

sorry, should be y= ax^2+bx+c

Answer 10

yea, are they always linear?

Answer 11

sometimes this term vanishes, i.e when b=0, for example, y=x^2 is a valid eqn for parabola but it has no linear term

Answer 12

oh. continue

Answer 13

since we know the four choices have their own linear term, we can compute the linear term only and still have the solution

Answer 14

C?

Answer 15

if y=(ax+b)^2, the linear term is 2abx

Answer 16

what is the value for a and b in your case?

Answer 17

im super confused

Answer 18

so expand (x+3)^2, you get x^2+6x+9, agree?

Answer 19

how did u get this part x^2+6x+9,

Answer 20

(x+3)^2 is (x+3)(x+3)

Answer 21

which is x(x+3)+3(x+3) which is x^2+3x+3x+9, x^2+6x+9