SOLUTION: sketch the graph of f(x)=3(x-1)(x+4), state the x-intercepts and the co-ordinates of the vertex.

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Question 253501: sketch the graph of f(x)=3(x-1)(x+4), state the x-intercepts and the co-ordinates of the vertex.
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
When y =0, x=1 and x=-4
vertex= (-3/2,-75/4)=(-1.5,-18.75)
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y = 3 x^2+9 x-12
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B9x%2B-12+=+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=%289%29%5E2-4%2A3%2A-12=225.

Discriminant d=225 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-9%2B-sqrt%28+225+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%289%29%2Bsqrt%28+225+%29%29%2F2%5C3+=+1
x%5B2%5D+=+%28-%289%29-sqrt%28+225+%29%29%2F2%5C3+=+-4

Quadratic expression 3x%5E2%2B9x%2B-12 can be factored:
3x%5E2%2B9x%2B-12+=+3%28x-1%29%2A%28x--4%29
Again, the answer is: 1, -4. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B9%2Ax%2B-12+%29