4x + 2x = < y
This is because the opposite sides (which is 4x and 2x) of a triangle add up to the exterior angle (<y).
We have to find X.
As you know:
because the angles of a triangle add up to 180.
When we add them:
The 9 is multiplying with the X. We want X only and not 9 with it. So, when we take 9 to the other side, it becomes divide. As a result, the answer to x is:-
Substitute value of x into 4x and 2x to find the exterior angle:-
4x:
2x:
When we add them we get the answer for angle Y:-
Therefore, we can conclude that:
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
