Answers:
- Vertex form: y = -2(x-1)^2 + 8
- Standard form: y = -2x^2 + 4x + 6
Pick whichever form you prefer.
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Explanation:
The vertex is the highest point in this case, which is located at (1,8).
In general, the vertex is (h,k). So we have h = 1 and k = 8.
One root of this parabola is (-1,0). So we'll plug x = -1 and y = 0 in as well. As an alternative, you can go for (x,y) = (3,0) instead.
Plug those four values mentioned into the equation below. Solve for 'a'.
y = a(x-h)^2 + k
0 = a(-1-1)^2+8
0 = a(-2)^2+8
0 = 4a+8
4a+8 = 0
4a = -8
a = -8/4
a = -2
The vertex form of this parabola is y = -2(x-1)^2+8
Expanding that out gets us the following
y = -2(x-1)^2+8
y = -2(x^2-2x+1)+8
y = -2x^2+4x-2+8
y = -2x^2+4x+6 .... equation in standard form
You know angles B and C are both 60°, the values of the angles in an equilateral triangle. Since the sum of angles in a quadrilateral is 360°, you have
B + C + x + y = 360°
60° +60° + x + y = 360°
x + y = 240°
Both trains travel for 7 time units.
Train A travels 385 distance units, so its speed is
Train B travels 577.5 distance units, so its speed is
Note that the units are not specified, but considering that we're talking about trains, the graph is likely to be showing distance in km (or miles) and time in hours.
Also, the distance traveled by train B is not perfectly aligned with the grid, so I assumed that it was the average between the two ticks of 550 and 605.
Answer:
815/1000=163/200 is the simplest form.
