Graph the following function and identify any shifts, stretches, and symmetry and x and y intercepts:

y = f(x) = (x - 3)^2 + 2

Step-by-step explanation:

The parent function here is y = x^2, whose graph is that of a parabola that opens up and has its vertex at the origin, (0, 0).

Translating this parent graph 3 units to the right and then up by 2 units will produce the desired graph of y = f(x) = (x - 3)^2 + 2.

There are no stretches or symmetry.

y-intercept:  let x = 0 and find y:  9 + 2 = 11.  y-intercept is (0, 11).

x-intercept:  let y = 0 and find x:  (x - 3)^2 + 2 = 0 => (x - 3)^2 = -2.  This has no real roots.  Thus, there are no x-intercepts.

a variable is any characteristics, number, or quantity that can be measured or counted. a variable may also be called a data item. hope i !

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240