Again X-intercept_Help@@@@

[m51v50]

Does Y=a(X+h)^ 2+k intersects with axis-x?
1). h=0
2). k=0

Explanations are highly appreciated.....

[VP_Tatiana]

For 1), we plug h=0 into the formula. This gives us:
Y = ax^2+k

With this formula, we could have the situation where the line crosses the X axis, such as when a = 0. Then Y = 0 for every X; it essentially equals the X axis.

We could also have the situation where the line does not cross the X axis, such as when a = 1 and k = -2. If we plug these into our formula, we get:
Y = 1* x^2-2. This is Y = x^0, or Y = 1. This is never 0, so it never crosses the X axis.

Thus, 1 does not give us sufficient information.

For 2), we plug k = 0 into the formula. This gives us:
Y = a(x + h)^2

Again, if a = 0 then the line is essentially equal to the x axis. No matter what h is, we can find an x (equal to -h) such that Y = 0. Thus, in 2) we are guaranteed that the line will cross the X axis. 2 is sufficient.

Thus, the answer is B.

[chidcguy]

Please use parentheses to clearly show the exponent

I did the problem initially with y=a(x+h) ^2 + k. I guess the original intent is

y=a(x+h) ^ (2+k)

Good problem and the (2) explanation is great