SOLUTION: determine the set of values of k for which the line 2y=x+k does not intersect the curve y=x^2-4x+7

Question 524256: determine the set of values of k for which the line 2y=x+k does not intersect the curve y=x^2-4x+7
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
determine the set of values of k for which the line 2y=x+k does not intersect the curve y=x^2-4x+7
-----
Since the quadratic opens up you cannot get above it for all values of "x".
So go below it.
---
The minimum of the quadratic occurs when x = -b/(2a) = 4/2 = 2
f(2) = 4-8+7 = 3
---
Minimum at (2,3)
----
Find the line equation where 2y=x+k passing thru (2,3)
---
2*3 = 2+k
k = 4
-----
Equation:
2y= x+4
y = (1/2)x+2
----
Answer: k < 4
======================
Cheers,
Stan H.
===============
RELATED QUESTIONS
Determine the set of values of the constant k for which the line y = 4x + k does not... (answered by Alan3354,ikleyn)

Find the range of values of k, such that the straight line {{{y=3x+k}}} does not... (answered by greenestamps,JaydenX)

Find the range of values of K for which the line {{{y+kx+9=0}}} does not intersect the... (answered by robertb)

The equation of a curve xy = 12 and the equation of a line L is 2x + y = k, where k is a (answered by math_tutor2020)

Determine the k values such that y= 4x + k does not intersect the parbola y=-3x^2 -x... (answered by solver91311)

Find the values of k for which the line y=kx-10 meets the curve... (answered by MathLover1,ikleyn)

Show that there are no values of k for which the line y=3-2x can intersect the curve... (answered by ikleyn)

For what values of 'k' is the line y=x tangent to the curve with equation y=k/(x-1)... (answered by robertb)

If the line y + 2x = p does not intersect the curve y^2 = x + p, find the range of values (answered by Edwin McCravy,MathLover1)