SOLUTION: How would I do this complicated problem? Use the Equation:{{{y=x^2-2x-3}}} to complete the following a) Find the x - intercepts b) Find the y - intercepts c) Find the Verte

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: How would I do this complicated problem? Use the Equation:{{{y=x^2-2x-3}}} to complete the following a) Find the x - intercepts b) Find the y - intercepts c) Find the Verte      Log On


   

Question 1041928: How would I do this complicated problem?
Use the Equation:y=x%5E2-2x-3 to complete the following
a) Find the x - intercepts
b) Find the y - intercepts
c) Find the Vertex
d) Use the information from parts a,b and c to sketch a graph..
I greatly appreciate any and all help very much
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
y=x%5E2-2x-3
(a)
The x-intercepts occur where +y+=+0+, so
+x%5E2+-+2x+-+3+=+0+
+%28+x+-+3+%29%2A%28+x+%2B+1+%29+=+0+
( with practice, you can factor just by examination )
+x+=+3+
+x+=+-1+
So, the x-intercepts are at
( 3,0 )
( -1,0 )
------------------------
(b)
The y-intercepts occur where +x+=+0+, so
+y+=+0%5E2+-+2%2A0+-+3+
+y+=+-3+
There is one y-intercept at
(0,-3)
-------------------------
(c)
The formula for the x-value of the vertex is:
+x%5Bv%5D+=+-b%2F%282a%29+
+x%5Bv%5D+=+-%28-2%29+%2F+%282%2A1%29+
+x%5Bv%5D+=+1+
Plug this value back into equation
+y%5Bv%5D+=+1%5E2+-+2%2A1+-3+
+y%5Bv%5D+=+1+-+2+-+3+
+y%5Bv%5D+=+-4+
The vertex is at
( 1,-4 )
-----------------------------
(d)
The plot is:
+graph%28+400%2C+400%2C+-6%2C+6%2C+-6%2C+10%2C+x%5E2+-+2x+-+3+%29+