\[
m=8-1
\]
6. If quadratic function $y=x^{2}-2 x+3-a$ has only one intersection with $x$-axis. Find the value of a

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Final Answer: $a = \boxed{2}$

Steps

Step 1 ：The quadratic function intersects the x-axis at the roots of the equation. If the function only has one intersection with the x-axis, it means that the quadratic equation has exactly one solution. This happens when the discriminant of the quadratic equation is equal to zero.

Step 2 ：The discriminant of a quadratic equation of the form $ax^2 + bx + c = 0$ is given by $b^2 - 4ac$. In this case, $a=1$, $b=-2$, and $c=3-a$.

Step 3 ：We need to solve the equation $(-2)^2 - 4*(1)*(3-a) = 0$ for $a$.

Step 4 ：Solving the equation gives us $a = 2$.

Step 5 ：Final Answer: $a = \boxed{2}$

\[m=8-1\]6. If quadratic function $y=x^{2}-2 x+3-a$ has only one intersection with $x$-axis. Find the value of a

Answer

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\[
m=8-1
\]
6. If quadratic function $y=x^{2}-2 x+3-a$ has only one intersection with $x$-axis. Find the value of a