SOLUTION: Graph f(x) = -x^2+4x-3, labeling the y-intercept, vertex, and axis of symmetry.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Graph f(x) = -x^2+4x-3, labeling the y-intercept, vertex, and axis of symmetry.      Log On


   

Question 43480: Graph f(x) = -x^2+4x-3, labeling the y-intercept, vertex, and axis of symmetry.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Graph f(x) = -x^2+4x-3, labeling the y-intercept, vertex, and axis of symmetry
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -1x%5E2%2B4x%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=%284%29%5E2-4%2A-1%2A-3=4.

Discriminant d=4 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-4%2B-sqrt%28+4+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%284%29%2Bsqrt%28+4+%29%29%2F2%5C-1+=+1
x%5B2%5D+=+%28-%284%29-sqrt%28+4+%29%29%2F2%5C-1+=+3

Quadratic expression -1x%5E2%2B4x%2B-3 can be factored:
-1x%5E2%2B4x%2B-3+=+-1%28x-1%29%2A%28x-3%29
Again, the answer is: 1, 3. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-1%2Ax%5E2%2B4%2Ax%2B-3+%29

Y=intercept= (0,-3)
Axis of symmetry = x=-b/2a=-4/(-2)=2
Vertex is on the graph.
Cheers,
Stan H.