SOLUTION: how do i graph? 1) y=4(x-6)(x-4) 2) y=3(x+4)(x+3) 3) y=3(x+5)(x=4) 4) y+4(x-4)(x-2) 5) y=4(x-7)(x-5)

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Question 111184: how do i graph?
1) y=4(x-6)(x-4)

2) y=3(x+4)(x+3)
3) y=3(x+5)(x=4)
4) y+4(x-4)(x-2)
5) y=4(x-7)(x-5)
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
First set y+=+0, then multiply terms on the right side
1.
y+=+4%28x-6%29%28x-4%29+….. if y+=+0, then we will have:
y+=+4%28x-6%29%28x-4%29+…………. multiply terms on the right side
0+=+4%2A%28x%5E2+%2B%28-4x%29%2B%28-6x%29+%2B+24%29
0+=+4x%5E2-40x%2B96

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 4x%5E2%2B-40x%2B96+=+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=%28-40%29%5E2-4%2A4%2A96=64.

Discriminant d=64 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--40%2B-sqrt%28+64+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-40%29%2Bsqrt%28+64+%29%29%2F2%5C4+=+6
x%5B2%5D+=+%28-%28-40%29-sqrt%28+64+%29%29%2F2%5C4+=+4

Quadratic expression 4x%5E2%2B-40x%2B96 can be factored:
4x%5E2%2B-40x%2B96+=+%28x-6%29%2A%28x-4%29
Again, the answer is: 6, 4. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B-40%2Ax%2B96+%29


2)
y+=3%28x%2B4%29%28x%2B3%29+….. if y+=+0, then we will have:
y+=3%28x%2B4%29%28x%2B3%29+……… multiply terms on the right side
0+=3%28x%5E2+%2B+3x+%2B4x+%2B+12%29
0+=3x%5E2+%2B+9x+%2B12x+%2B+36%29
0+=3x%5E2+%2B+21x+%2B+36%29

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B21x%2B36+=+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=%2821%29%5E2-4%2A3%2A36=9.

Discriminant d=9 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-21%2B-sqrt%28+9+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2821%29%2Bsqrt%28+9+%29%29%2F2%5C3+=+-3
x%5B2%5D+=+%28-%2821%29-sqrt%28+9+%29%29%2F2%5C3+=+-4

Quadratic expression 3x%5E2%2B21x%2B36 can be factored:
3x%5E2%2B21x%2B36+=+%28x--3%29%2A%28x--4%29
Again, the answer is: -3, -4. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B21%2Ax%2B36+%29



3)
y=3%28x%2B5%29%28x-4%29…… if y+=+0, then we will have:
0+=3%28x%2B5%29%28x-4%29………… multiply terms on the right side

0+=+3%2A%28x%5E2+%2B%28-4x%29%2B5x+%2B+20%29

0+=3%28x%5E2++%2B+x+-+20%29
y=3x%5E2++%2B+3x+-+60

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B3x%2B60+=+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=%283%29%5E2-4%2A3%2A60=-711.

The discriminant -711 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


In the field of imaginary numbers, the square root of -711 is + or - sqrt%28+711%29+=+26.6645832519468.

The solution is , or
Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B3%2Ax%2B60+%29



4)
y=4%28x-4%29%28x-2%29+…….. if y+=+0, then we will have:
0+=4%28x-4%29%28x-2%29+……… multiply terms on the right side
0+=+4%2A%28x%5E2+%2B%28-2x%29%2B%28-4x%29+%2B+8%29
0+=4%28x%5E2++-6x+%2B+8%29

0+=+4x%5E2-+24x+%2B+32


Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 4x%5E2%2B-24x%2B32+=+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=%28-24%29%5E2-4%2A4%2A32=64.

Discriminant d=64 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--24%2B-sqrt%28+64+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-24%29%2Bsqrt%28+64+%29%29%2F2%5C4+=+4
x%5B2%5D+=+%28-%28-24%29-sqrt%28+64+%29%29%2F2%5C4+=+2

Quadratic expression 4x%5E2%2B-24x%2B32 can be factored:
4x%5E2%2B-24x%2B32+=+%28x-4%29%2A%28x-2%29
Again, the answer is: 4, 2. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B-24%2Ax%2B32+%29



5)

y=4%28x-7%29%28x-5%29…….. if y+=+0, then we will have:
0+=4%28x-7%29%28x-5%29……… multiply terms on the right side
0+=+4%2A%28x%5E2+%2B%28-5x%29%2B%28-7x%29+%2B+35%29

0+=4%28x%5E2++-+12x+%2B+35%29

0+=+4x%5E2-48x%2B+140



Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 4x%5E2%2B-48x%2B140+=+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=%28-48%29%5E2-4%2A4%2A140=64.

Discriminant d=64 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--48%2B-sqrt%28+64+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-48%29%2Bsqrt%28+64+%29%29%2F2%5C4+=+7
x%5B2%5D+=+%28-%28-48%29-sqrt%28+64+%29%29%2F2%5C4+=+5

Quadratic expression 4x%5E2%2B-48x%2B140 can be factored:
4x%5E2%2B-48x%2B140+=+%28x-7%29%2A%28x-5%29
Again, the answer is: 7, 5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B-48%2Ax%2B140+%29