Answer:
ABOVE the x-axis
Step-by-step explanation:
Please use "^" to denote exponentiation: y = x^2 + 2x + 3
To find the vertex, we must complete the square of y = x^2 + 2x + 3, so that we have an equivalent equation in the form f(x) = (x - h)^2 + k.
Starting with y = x^2 + 2x + 3,
we identify the coefficient of x (which is 2), take half of that (which gives
us 1), add 1 and then subtract 1, between "2x" and "3":
y = x^2 + 2x + 1 - 1 + 3
Now rewrite x^2 + 2x + 1 as (x + 1)^2:
y = (x + 1)^2 - 1 + 3, or y = (x + 1)^2 + 2. Comparing this to f(x) = (x - h)^2 + k, we see that h = 1 and k = 2. This tells us that the vertex of this parabola is at (h, k): (1, 2), which is ABOVE the x-axis.
Answer:
x = 5
Step-by-step explanation:
4x + 2y + z = 24
2x - 3y - z = 2
5x + y + 2z = 21
-----------------
Eliminate z
Add the 1st and 2nd eqn
4x + 2y + z = 24
2x - 3y - z = 2
----------------
6x - 1y = 26 eqn A
Multiply the 2nd eqn by 2, then add the 3rd.
4x - 6y -2z = 4
5x + y + 2z = 21
----------------
9x - 5y = 25 eqn B
---------------
Now you have 2 eqns in 2 unknowns, not 3.
Multiply eqn A by 5 and subtract eqn B.
30x - 5y = 130 eqn A times 5
9x - 5y = 25 eqn B
-------------
21x = 105
x = 5
Answer:
2 minutes
Step-by-step explanation:
Answer:
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Step-by-step explanation:
