SOLUTION: I have been working on this math problem and I can't seem to figure it out. I was wondering if someone could help me? Please and Thank You!! I would deeply appreciate it!! Find

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Question 184808This question is from textbook Algebra and Trigonometry Structure and Method book 2
: I have been working on this math problem and I can't seem to figure it out. I was wondering if someone could help me? Please and Thank You!! I would deeply appreciate it!!
Find all intercepts of the parabola y-2=-1/2(x-4)^2 This question is from textbook Algebra and Trigonometry Structure and Method book 2

Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!

Given: y-2=-1%2F2%28x-4%29%5E2--->y-2=%28-1%2F2%29%28x%5E2-8x%2B16%29, distribute -1%2F2 and transfer -2 to the right.
y=%28-1%2F2%29x%5E2-%28-8%2F2%29x%2B%28-16%2F2%29%2B2=%28-1%2F2%29x%5E2%2B4x-8%2B2
y=%28-1%2F2%29x%5E2%2B4x-6, EQN 1
First, we'll find the vertex thru Vertex form: y=a%28x-h%29%5E2%2Bk%5E2
wheresystem%28h=x%2Ck=y%29 of the vertex
we complete the square:
Divide the whole eqn by -1%2F2:
y%2F%28-1%2F2%29=%28%28-1%2F2%29x%5E2%2B4x-6%29%2F%28-1%2F2%29--->
-2y=x%5E2-8x%2B12
-2y=%28x%5E2-8x%2Bhighlight%2816%29%29%2B12-highlight%2816%29
-2y=%28x-4%29%5E2-4
cross%28-2%29y%2Fcross%28-2%29=%28%28x-4%29%5E2-4%29%2F-2
y=%28-1%2F2%29%28x-4%29%5E2-%284%2F-2%29
y=%28-1%2F2%29%28x-4%29%5E2%2B2
You see, highlight%28h=x=4%29 & highlight%28k=y=2%29--->VERTEX (4,2)
Next:
Let Fx=0, as per EQN 1
y=%28-1%2F2%29%280%29%5E2%2B4%280%29-6
highlight%28y=-6%29, Y Intercept
Next:
For the X Intercepts, we solve the Eqn1:
by QUADRATIC, wheresystem%28a=-1%2F2%2Cb=4%2Cc=-6%29
Solving for he discriminant: b%5E2-4ac=4%5E2-4%28-1%2F2%29%28-6%29=16-12=4
Therefore,
x=%28-4%2B-sqrt%284%29%29%2F%282%2A-1%2F2%29=%28-4%2B-2%29%2F-1
x=%28-4%2B2%29%2F-1=-2%2F-1=highlight%282%29
Also, x=%28-4-2%29%2F-1=-6%2F-1=highlight%286%29
Then we see the graph, plotting all intercepts:

Thank you,
Jojo