Answer:
1r + 8(400) = 3(r+400)
1r + 320 = 3r + 120
2r = 200
r = 200 / 2 = 1000
1400 * 3 = 420
100 + 320 = 420
Step-by-step explanation:
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
Answer:
Z equals 16. Hope this helps!
If you knew calculus this problem would take like 2 seconds, but since we are working with maybe Algebra 2, you have to use the equation as it is and find where h(x) is 0, because that is the height of something when it hits the ground. Meaning, you have to factor this and solve it for x. Here's your equation:
h(x) = -16x^2 + 60x +16. Use the quadratic formula to find that the values for x are -.25 and 4 seconds. Of course time cannot ever carry a negative value, so the answer is 4 seconds. It takes the ball 4 seconds to hit the ground.
