Answer:
k = 1
Step-by-step explanation:
Discriminant
[tex]b^2-4ac\quad\textsf{when }\:ax^2+bx+c=0[/tex]
[tex]\textsf{when }\:b^2-4ac > 0 \implies \textsf{two real roots}[/tex]
[tex]\textsf{when }\:b^2-4ac=0 \implies \textsf{one real root}[/tex]
[tex]\textsf{when }\:b^2-4ac < 0 \implies \textsf{no real roots}[/tex]
As we need to determine the value of k that will give one solution, set the discriminant to zero.
Given equation:
[tex]y=kx^2-4x+4[/tex]
Therefore:
Substitute these values into the discriminant and solve for k:
[tex]\begin{aligned}b^2-4ac & = 0\\\implies (-4)^2-4(k)(4) & = 0\\16-16k & = 0\\16k & = 16\\\implies k & = 1\end{aligned}[/tex]
