Find the orthogonal decomposition of vector b = 9, 0, 0 with respect to vector a = 4, −5, 0 . (Your instructors prefer angle bracket notation < > for vectors.)

The orthogonal componentes of with respect to are and , respectively.

Step-by-step explanation:

Let be and , the component of parallel to is found by the following expression:

Where means for dot product and is the unit vector of , which is determined by:

Where is the norm of , which can be found by Pythagorean Theorem.

The vector of parallel to vector is now determined:

Now, the component of perpendicular to is obtained by vector subtraction:

Given that and , the expression for the remaining component is:

The orthogonal componentes of with respect to are and , respectively.

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1

the 3rd on is correct

step-by-step explanation: