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)   (Show Source): You can put this solution on YOUR website!
First set , then multiply terms on the right side
1.
….. if , then we will have:
…………. multiply terms on the right side



Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=64 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 6, 4. Here's your graph:


2)
….. if , then we will have:
……… multiply terms on the right side




Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=9 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: -3, -4. Here's your graph:



3)
…… if , then we will have:
………… multiply terms on the right side






Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

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 - .

The solution is , or
Here's your graph:



4)
…….. if , then we will have:
……… multiply terms on the right side






Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=64 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 4, 2. Here's your graph:



5)

…….. if , then we will have:
……… multiply terms on the right side








Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=64 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 7, 5. Here's your graph:
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