1.

An alternative way of solving problems.Use discriminant to find the minimum value of . Thank you for solving my problems!Hint: touches each other for certain value of k, and 'touching' means have at least one solution.

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ANSWER:

y=f(x) is a parabola

y=ky=k is a HORIZONTAL line

If two intersects, that will be the solution of the system equation of

\begin{gathered}\begin{cases} & y=k \\ & y=f(x) \end{cases}\end{gathered}

{

y=k

y=f(x)

So LET's solve the system equation.

f(x)=kf(x)=k

\longleftrightarrow 2x^2-7x+2=k⟷2x

2

−7x+2=k

\longleftrightarrow 2x^2-7x-k+2=0⟷2x

2

−7x−k+2=0

\boxed{D=33+8k\geq 0}

D=33+8k≥0

Thus, y=ky=k intersects if and only if k\geq -\dfrac{33}{8}k≥−

8

33

. So, the lowest location of the horizontal line is y=-\dfrac{33}{8}y=−

8

33

, so it is the minimum value.


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