The Parabola P has equation y =- x ^ 2 +2 x-3 and the function f has the rule f (x) = 2x ^ 2-8x + k
a) Determine the intersection between P and f
b) Determine k so that the graphs of f and P has exactly one common point
Please help me and explain! Thanks a lot..
a) Determine the intersection between P and f
b) Determine k so that the graphs of f and P has exactly one common point
Please help me and explain! Thanks a lot..
-
y = -x² + 2x - 3
f(x) = 2x² - 8x + k
P and f intersect when
2x² - 8x + k = -x² + 2x - 3
3x² - 10x + k+3 = 0
Use the quadratic equation to solve for x
x = [10±√(10² - 4·3(k+3))]/(2·3)
= [10±√(100 - 12k-36)]/6
= [10±√(64 - 12k)]/6
There is one value for x when 64 - 12k = 0
k = 5⅓
P and f intersect at exactly one point when k = 5⅓.
The x-coordinate of the point of intersection is
x = [10±√(64 - 12(5⅓))]/6
= 10/6
= 1⅔
The y-coordinate of the point of intersection is
y = -(1⅔)² + 2(1⅔) - 3 = -22/9
http://www.flickr.com/photos/dwread/6066…
f(x) = 2x² - 8x + k
P and f intersect when
2x² - 8x + k = -x² + 2x - 3
3x² - 10x + k+3 = 0
Use the quadratic equation to solve for x
x = [10±√(10² - 4·3(k+3))]/(2·3)
= [10±√(100 - 12k-36)]/6
= [10±√(64 - 12k)]/6
There is one value for x when 64 - 12k = 0
k = 5⅓
P and f intersect at exactly one point when k = 5⅓.
The x-coordinate of the point of intersection is
x = [10±√(64 - 12(5⅓))]/6
= 10/6
= 1⅔
The y-coordinate of the point of intersection is
y = -(1⅔)² + 2(1⅔) - 3 = -22/9
http://www.flickr.com/photos/dwread/6066…