For the function : f(x) = -(x-2)^2+9 name all transformations, intercepts and the vertex

Given:

The given function is:

To find:

The transformations, intercepts and the vertex.

Solution:

The vertex form of a parabola is:

        ...(i)

Where, a is a constant and (h,k) is vertex.

If a<0, then the graph of parent quadratic function reflect across the x-axis.

If h<0, then the graph of parent function shifts h units left and if h>0, then the graph of parent function shifts h units right.

If k<0, then the graph of parent function shifts k units down and if k>0, then the graph of parent function shifts k units up.

We have,

         ...(ii)

On comparing (i) and (ii), we get

So, the graph of the parent function reflected across the x-axis, and shifts 2 units right and 9 units up.

Putting x=0 in (ii), we get

The y-intercept is 5.

Putting f(x)=0 in (ii), we get

Taking square root on both sides, we get

Therefore, the x-intercepts are -1 and 5.

The values of h and k are 2 and 9 respectively and (h,k) is the vertex of the parabola.

Therefore, the vertex of the parabola is (2,9).

19.

step-by-step explanation:

you add the 9 in the tens column since it is a single digit and 9 plus zero is 9 so it is 19

there are 70 more legs than eyes at the dog show (196 – 126 = 70). dogs have two more legs than eyes, and humans have the same number of legs as eyes. thus 70 is twice the number of dogs at the show, so the number of dogs is half of 70, which is 35. to get the number of humans, subtract 35 from 63: 63 – 35 = 28.

step-by-step explanation: