Question

Determine which of the following statements is true concerning the values described in column #1 and column #2.
Column #1
The x-coordinate of the vertex of the equation
y = 2x2 − 4x + 12
Column #2
The x-coordinate of the vertex of the equation
y = 4x2 + 8x + 3

Answer 1

Possible Answers

Possible Answers
1) The value found in column #1 is greater than the value found in column #2.
2)The value found in column #1 is less than the value found in column #2.
3) The value found in column #1 is equivalent to the value found in column #2
4) The relationship between column #1 and column #2 cannot be determined by the given info

Answer 2

before we answer the questions, why don't we find the coordinates of the vertex for each? i

Answer 3

the first coordinate of the vertex of \(ax^2+bx+c\) is \(-\frac{b}{2a}\)
compute the two numbers

Answer 4

for example, in \(y = 2x^2 − 4x + 12\) we have \(a=2,b=-4\) and so
\[-\frac{b}{2a}=-\frac{-4}{2\times 2}=-1\]

Answer 5

sorry that was wrong
it is
\[-\frac{2}{2a}=-\frac{-4}{2\times 2}=1\] not \(-1\) that was my mistake

Answer 6

Ok I think i'm following you so far.

Answer 7

good then you only have one more to do
compute the vertex the same way for \[y = 4x^2 + 8x + 3 \]
that is, compute \(-\frac{b}{2a}\) for \(a=4,b=8\) let me know what you get

Answer 8

and this would be where I lost you lol

Answer 9

I believe the answer is the first choice. Is this right or wrong?

Answer 10

did you calculate
\[-\frac{8}{2\times 4}\]?

Answer 11

Yes

Answer 12

what did you get?

Answer 13

i hope you got \(-1\)
so you are right, the first answer is correct,

Answer 14

-1

Answer 15

Ok thank you!