SOLUTION: Sketch a graph of the quadratic function. f(x) = x^2 − 2x − 1 Give the vertex, axis of symmetry, and intercepts. (If an answer does not exist, enter DNE.)

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Sketch a graph of the quadratic function. f(x) = x^2 − 2x − 1 Give the vertex, axis of symmetry, and intercepts. (If an answer does not exist, enter DNE.)       Log On


   

Question 1071430: Sketch a graph of the quadratic function.
f(x) = x^2 − 2x − 1
Give the vertex, axis of symmetry, and intercepts. (If an answer does not exist, enter DNE.)
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Factorable? Discriminant, %28-2%29%5E2-4%2A1%2A%28-1%29=4%2B4=8. Not really factorable.

Complete the Square to put into standard form.

x%5E2-2x%2B1-1-1
%28x-1%29%5E2-2
-----
f%28x%29=%28x-1%29%5E2-2------vertex is at (1,-2).

Symmetry Axis: at x=1.


Intercepts?
%28x-1%29%5E2=2
x-1=0%2B-+sqrt%282%29
x=1%2B-+sqrt%282%29
-
You can also look for a y-intercept, by letting x=0 and evaluate y. Find f(0).

ANSWER SUMMARY
Vertex (1,-2)
Axis Of Symmetry x=1
Roots 1%2B-+sqrt%282%29

graph%28300%2C300%2C-3%2C5%2C-5%2C3%2Cx%5E2-2x-1%29