SOLUTION: Find the x intercepts y = x^2 - 3x - 1 I do not understand how I am to find the intercepts formula, can anyone help me out on this one please, thank you!

Algebra ->  Equations -> SOLUTION: Find the x intercepts y = x^2 - 3x - 1 I do not understand how I am to find the intercepts formula, can anyone help me out on this one please, thank you!      Log On


   

Question 69894: Find the x intercepts
y = x^2 - 3x - 1
I do not understand how I am to find the intercepts formula, can anyone help me out on this one please, thank you!
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Find the x intercepts
y = x^2 - 3x - 1
:
The x intercepts occur when y = 0, (when a graph crosses the x axis)
:
x^2 - 3x - 1 = 0; solve for x, the solutions will be the x intercepts
:
This equation cannot be factored so you have to find x using the quadratic formula
In this equation a = 1 b = -3; c = -1
:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
:
x+=+%28-%28-3%29+%2B-+sqrt%28+-3%5E2-+4+%2A+1+%2A+-1+%29%29%2F%282%2A1%29+
:
x+=+%28%2B3+%2B-+sqrt%28+9+-+%28-4%29+%29%29%2F%282%29+
:
x+=+%28%2B3+%2B-+sqrt%28+9+%2B+4+%29%29%2F%282%29+
:
x+=+%28%2B3+%2B-+sqrt%28+13+%29%29%2F%282%29+
:
x+=+%28%2B3+%2B-+3.6%29%2F%282%29+
:
2 solutions:
x+=+%28%2B3+%2B+3.6%29%2F%282%29+
x+=+%28%2B6.6%29%2F%282%29+
x = +3.3
and
x+=+%28%2B3+-+3.6%29%2F%282%29+
x+=+%28-.6%29%2F%282%29+
x = -.3
:
x = +3.3 and -.3; these are the x intercepts as illustrated in this graph:
+graph%28+300%2C+200%2C+-3%2C+8%2C+-8%2C+8%2C+x%5E2+-+3x+-+1%29+
:
Notice that the graph "intercepts" the x axis at -.3 and + 3.3
:
Can you understand this now?