Which equation represents a parabola that opens upward, has a minimum at x = 3, and has a line of symmetry at x = 3?
2 answers:
Answer:
is the correct answer.
Step-by-step explanation:
We know that vertex equation of a parabola is given as:
where is the vertex of the parabola and
are the coordinate of points on parabola.
As per the question statement:
The parabola opens upwards that means coefficient of is positive.
Let
Minimum of parabola is at x = 3.
The vertex is at the minimum point of a parabola that opens upwards.
Putting value of a and h in the equation:
Formula used:
Comparing the equation formulated above with the options given we can observe that the equation formulated above is most similar to option A.
Comparing and
13 = 9+k
k = 4
Please refer to the graph attached.
Hence, correct option is
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Answer:
a)
S+G=525
G=S+75
b) See attached pictures
c) S=$225 and G=$300
The point where both graphs meet each other is the point where both equations will be true when having the same S and G values. This is, this is the point where both conditions given by the problem are the same.
Step-by-step explanation:
a) For the first part of the problem, the addition of both amounts will give us the total, so the first equation is:
S+G=525.
On the second equation we need to add 75 to sharon's amount to figure Geordi's amount, so we get:
G=S+75
b) In order to graph the system of equations, we need to find two points for each of the equations. It would be a good idea to solve the first equation for g, so our system of equations would be:
G=525-S
G=S+75
First Equation:
You can pick any value you like for S, for example: S=0 and then substitute it into the equation to get te first G-value:
G=525-0
so G=525.
So the first ordered pair would be (0,525)
You can do the same with a different S-value to get a second point to plot:
S=100
G=525-100
G=424
so the second ordered pair would be (100,424)
and now you can plot the points on the graph and connect them with a straight line.
See attached picture.
Second Equation:
The same procedure is followed for the second equation, in this case I used the same S-values, but you can use different values if you wish, so the two points to plot were:
(0,75)
(100,175)
and the graph looks like the one attached.
c)
In order to figure out how much each person earned, we need to find the point where the two graphs meet each other (see attached picture) in this case the point will be located at (225,300)
This means that Sharon earned a total of $225 while Geordi earned a total of $300.
S=$225 and G=$300
The point where both graphs meet each other is the point where both equations will be true when having the same S and G values. This is, this is the point where both conditions given by the problem are the same.
