SOLUTION: Find the vertex of each equation ! PLEASE HELP SOMEONE !!! 1. h(x) = (x + 2)2 – 1 2. h(x) = (x + 1)2 – 2 3. h(x) = (x - 2)2 - 1 4. h(x) = (x - 1)2 – 2 5. h(x) =

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Find the vertex of each equation ! PLEASE HELP SOMEONE !!! 1. h(x) = (x + 2)2 – 1 2. h(x) = (x + 1)2 – 2 3. h(x) = (x - 2)2 - 1 4. h(x) = (x - 1)2 – 2 5. h(x) =       Log On


   



Question 795063: Find the vertex of each equation ! PLEASE HELP SOMEONE !!!
1. h(x) = (x + 2)2 – 1
2. h(x) = (x + 1)2 – 2
3. h(x) = (x - 2)2 - 1
4. h(x) = (x - 1)2 – 2
5. h(x) = (x + 2)2 + 1
6. h(x) = (x + 1)2 + 2

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The vertex is right there, in front of your eyes.
I'll show you how to look for it.
1. h%28x%29+=+%28x+%2B+2%29%5E2+%96+1+ is -1 when x=-2,
because then %28x%2B2%29%5E2=0%5E2=0.
For all other values of x,
%28x%2B2%29%5E2%3E0 and h%28x%29+=+%28x+%2B+2%29%5E2+%96+1%3E-2+.
So (-2,-1), with x=-2 and y=%28-2%2B2%29%5E-1=-1 is the minimum and the vertex.

2. h%28x%29+=+%28x+%2B+1%29%5E2+%96+2 has a minimum and vertex at (-1,-2), because
when x=-1 h%28x%29=%28x+%2B+1%29%5E2+%96+2 takes the minimum value
h%28x%29=%28-1+%2B+1%29%5E2+%96+2=0%5E2-2=-2

3. h%28x%29+=+%28x+-+2%29%5E2+-+1 has a maximum and vertex at (2,-1).

4. h%28x%29+=+%28x+-+1%29%5E2+%96+2 has a maximum and vertex at (1,-2)

5. h%28x%29+=+%28x+%2B+2%29%5E2+%2B+1 has a maximum and vertex at (-2,1)

6. h%28x%29+=+%28x+%2B+1%29%5E2+%2B+2 has a maximum and vertex at (-1,2)

NOTES:
If you had a minus sign in front of that square, as in
f%28x%29=-2%28x-3%29%5E2%2B4 the vertex, at (3,4) in this case, would be a maximum, because for x%3C%3E3 -2%28x-3%29%5E2%3C0 and h%28x%29=-2%28x-3%29%5E3%2B4%3C4=h%283%29

When they give you the function as
h%28x%29=x%5E2%2B2x%2B3 you will have to transform it to the form given above
h%28x%29=x%5E2%2B2x%2B3=x%5E2%2B2x%2B1%2B2=%28x+%2B+1%29%5E2+%2B+2 to find the vertex.

You an write your exponents with a "^" in front, as in
h(x) = (x + 1)^2 + 2 , and everyone will know you mean h%28x%29+=+%28x+%2B+1%29%5E2+%2B+2