Question

THIS IS URGENT PLZZ HELP

Two quadratic functions are shown.

Function 1:
f(x) = 3x2 + 6x + 7 Function 2:

x g(x)
−2 13
−1 7
0 3
1 7


Which function has the least minimum value and what are its coordinates?
Function 1 has the least minimum value and its coordinates are (−1, 4).
Function 1 has the least minimum value and its coordinates are (0, 7).
Function 2 has the least minimum value and its coordinates are (−1, 7).
Function 2 has the least minimum value and its coordinates are (0, 3).

Answer 1

@ash2326 @paki @pooja195 @mathmate @myininaya

Answer 2

the answer is not c for future ppl

Answer 3

@egracer
In math, it's not about the correct answer, it's about how to do it so we learn something out of it. You will forget in two days about the mark that you get for this problem, but what you learn from it will stay forever.

For f(x)=3x2 + 6x + 7
You can find the minimum by
(A) completing the square
f(x)=3(x^2+2x)+7=3(x+1)^2-3+7=3(x+1)^2+4
This means that the minimum is located at x+1=0, or x=-1
Substitute in the function, f(-1)=3(-1)^2+6(-1)+7=4, so the coordinates are (-1,4)
(B) using calculus
we know that f(x) has a minimum when the leading coefficient of a quadratic is positive.
To locate it, we equate f'(x) to zero, or 6x+6=0, x=-1.
f(-1)=4 as before, so coordinates are (-1,4)

For g(x), we know that a quadratic is symmetric about its maximum/minimum.
we see very well that the location of symmetry occurs at
x y
−1 7
0 3
1 7
therefore the minimum is at (0,3).

I will leave that for you to choose the correct answer, even though perhaps the time has expired.
Good luck with your studies.