Can someone help me?

Question

so I am having issues with this problem

can someone help me how I would start it?

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

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

Answer 1

y=(x-3)^2+2

the parent function, y=x^2, shifts 3 units to the right (-3) and shifts 2 units up (+2)

note: shifting left or right is the opposite of what you would expect; negative is a shift to the right and positive is a shift to the left

Answer 2

y=(x-3)²+2

Compare this to the general form of the concave-vertical parabola: (x-h)²=4p(y-k)

(x-3)²=y-2

(x-h)²=4p(y-k)

This says that h=3, 4p=1, and k=2

The directrix is the line y=-1/4

The vertex (h,k)=(3,2) is the vertex

Since the coefficient on x² (1) is positive, the parabola is concave up.

y-intercept: when x=0, y=9+2=11

(0,11)

x-intercepts: when y=0, (x-3)²=-2 so there are no x-intercepts. The LHS is positive-definite and the RHS is negative-definite so the equality is untrue for all real values of x.

Summary:

a. function is a parabola due to the independent variable x being squared.

b. parabola is concave vertical because it is a quadratic of the form y=ax²+bx+c

c. parabola is concave-up because a>0.

d. parabola's vertex is at (3,2).

e. parabola's directrix is at y=-1/4

f. parabola's y-intercept is at (0,11)

g. there are no x-intercepts

I'll let you graph this.