SOLUTION: sketch graph of quadratic function f(x)=x^2-2x-3

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Question 633466: sketch graph of quadratic function
f(x)=x^2-2x-3


Found 3 solutions by stanbon, richwmiller, ewatrrr:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
sketch graph of quadratic function
f(x)=x^2-2x-3
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graph%28400%2C400%2C-10%2C10%2C-10%2C10%2Cx%5E2-2x-3%29
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Cheers,
Stan H.
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Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-2x%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=%28-2%29%5E2-4%2A1%2A-3=16.

Discriminant d=16 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--2%2B-sqrt%28+16+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+16+%29%29%2F2%5C1+=+3
x%5B2%5D+=+%28-%28-2%29-sqrt%28+16+%29%29%2F2%5C1+=+-1

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

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,



f(x) = x^2-2x-3  Pt(0,-3) on this parabola 

f(x) = (x-1)^2 -4  

parabola Opening upward, V(1,-4), Line of Symmetry x = 1

 0 = (x-1)^2 -4  , x-intercepts 1± 2,  Pts (3,0) and (-1,0) on the curve

Sketch: