SOLUTION: find y intercept and vertex: y = x^2 - 4x + 5

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: find y intercept and vertex: y = x^2 - 4x + 5      Log On


   

Question 114970: find y intercept and vertex: y = x^2 - 4x + 5
Answer by HyperBrain(694) About Me  (Show Source):
You can put this solution on YOUR website!
To find the y-intercept. Equate x=0.
Equating,
y=0%5E2-4%2A0%2B5=0%2B0%2B5=5

The y-intercept is at (0,5)

To find the vertex, read my lesson---Shortcut in finding the vertex of any parabola

IF y=x%5E2+-+4x+%2B+5, THEN dy%2F%28dx%29=2x-4

Equating this to ZERO,
2x-4=0
2x=4
x=2
Solving for y,
y=x%5E2+-+4x+%2B+5=2%5E2-4%2A2%2B5=4-8%2B5=-4%2B5=1

Thus, the vertex is at (2,1)

GRAPH:
graph%281000%2C1000%2C-20%2C20%2C-20%2C20%2Cx%5E2+-+4x+%2B+5%29

Power up,
HyperBrain!