Imagine that you are given the graph of a brand new parent function, y = P(x), that you have never seen before. You are then asked to graph y = P(x) + 3. Explain how you would go about graphing this new function.

You would move each point on y=P(x) up by three. Or add 3 to each y coordinate

Step-by-step explanation:

This is because we're not manipulating the value of x before it gets multiplied by P.

For example:

If x is set to equal 5 and P equal to 2, then the parent function would have a coordinate of (5,10) since 2(5)=10 but the new function would have a coordinate of (5,13) since 2(5)+3= 13 due to order of operations (2×5 =10, then we add 3).

Step-by-step explanation:

Step 1:

Plot y=P(x) from x=-a to x=a with x=0 as the middle point of the distance between a and -a.

Step 2:

Add the value of +3 to each point of y=P(x), ie, y=P(x)+3 meaning that the graph y=P(x) will be pulled up three units on the y axis.

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

we now create space between the x and y terms with parenthesis.

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

we add the squares to both sides.

simplify.

and write the quadratics in factored form.

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.