SOLUTION: Write the minimum or maximum point for each function and give the coordinates for that point 1. y=x^2-4+1___ hint start at 0 and increase. 2.y=x^2-8+5___ hint start at2 and increas

Algebra ->  Coordinate-system -> SOLUTION: Write the minimum or maximum point for each function and give the coordinates for that point 1. y=x^2-4+1___ hint start at 0 and increase. 2.y=x^2-8+5___ hint start at2 and increas      Log On


   

Question 161185: Write the minimum or maximum point for each function and give the coordinates for that point 1. y=x^2-4+1___ hint start at 0 and increase. 2.y=x^2-8+5___ hint start at2 and increase. 3. y=-x^2+2+6___ hint start at -1 and increase.I'm still in need of help with these if anyone can.
Answer by KnightOwlTutor(293) About Me  (Show Source):
You can put this solution on YOUR website!

The answer for question 1&2 are the same .They are the equivalent graphs:
Simplify each equation
1. y=X^2+(-4+1)=x^2-3
2.y=x^2+-8+5)=x^2-3

1.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B0x%2B-3+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%280%29%5E2-4%2A1%2A-3=12.

Discriminant d=12 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-0%2B-sqrt%28+12+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%280%29%2Bsqrt%28+12+%29%29%2F2%5C1+=+1.73205080756888
x%5B2%5D+=+%28-%280%29-sqrt%28+12+%29%29%2F2%5C1+=+-1.73205080756888

Quadratic expression 1x%5E2%2B0x%2B-3 can be factored:
1x%5E2%2B0x%2B-3+=+1%28x-1.73205080756888%29%2A%28x--1.73205080756888%29
Again, the answer is: 1.73205080756888, -1.73205080756888. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B0%2Ax%2B-3+%29


x^2-3=0
y+9/4=(x-3/2)^2
Plug in Values for x to get corresponding y values
y=-x^2+2+6
y-x^2+8
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -1x%5E2%2B0x%2B8+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%280%29%5E2-4%2A-1%2A8=32.

Discriminant d=32 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-0%2B-sqrt%28+32+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%280%29%2Bsqrt%28+32+%29%29%2F2%5C-1+=+-2.82842712474619
x%5B2%5D+=+%28-%280%29-sqrt%28+32+%29%29%2F2%5C-1+=+2.82842712474619

Quadratic expression -1x%5E2%2B0x%2B8 can be factored:
-1x%5E2%2B0x%2B8+=+-1%28x--2.82842712474619%29%2A%28x-2.82842712474619%29
Again, the answer is: -2.82842712474619, 2.82842712474619. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-1%2Ax%5E2%2B0%2Ax%2B8+%29

Plug in Values for x to get corresponding y values