Answer:
The equation of the transformed function is:
Step-by-step explanation:
We know that horizontal translation is of the form
where h is a constant
- When 'h' is positive, the function is shifted to the right.
-
When 'h' is negative, the function is shifted to the left.
From the given function, it is clear that h(x) is the horizontal translation. In other words, h(x) is the result of the horizontal shift of 3 units to the right.
Thus, the equation of the transformed function is:
Unit Rate is 6:
54 to 9
72 to 12
Unit Rate is 8:
72 to 9
Unit Rate is 10:
120 to 12
70 to 7
Doesn't belong to any category:
81 to 9
Answer: 67 on apex
Step-by-step explanation:
Directrix is a horizontal line, so the parabola is of the form
<span>(x-h)^2= 4p(y-k) , where (h,k) is the vertex </span>
<span>Coordinates of the focus is (h, k+p) </span>
<span>h = 8 (same as the focus) </span>
<span>k+p = -8 -----(1) </span>
<span>equation of directrix is y=k-p </span>
<span>k-p = -6 ------(2) </span>
<span>from (1) & (2) </span>
<span>2k = -14 </span>
<span>k=-7 </span>
<span>-7+p= -8 </span>
<span>p = -1 </span>
<span>vertex = (8,-7) </span>
<span>(x-8)^2 = -4(y+7) </span>
<span>y+7 = (-1/4) (x-8)^2 </span>
<span>y = (-1/4)(x-8)^2 - 7 is the parabola </span>
<span>What is the equation of the quadratic graph with a focus of (1, 1) and a directrix of y = −1? </span>
<span>Directrix is a horizontal line, so the parabola is of the form </span>
<span>(x-h)^2= 4p(y-k) , where (h,k) is the vertex </span>
<span>Coordinates of the focus is (h, k+p) </span>
<span>h = 1 (same as the focus) </span>
<span>k+p = 1 -----(1) </span>
<span>equation of directrix is y=k-p </span>
<span>k-p = -1 ------(2) </span>
<span>from (1) & (2) </span>
<span>2k = 0 </span>
<span>k=0 </span>
<span>0+p= 1 </span>
<span>p = 1 </span>
<span>vertex = (1,0) </span>
<span>(x-1)^2 = 4(y-0) </span>
<span>(x-1)^2=4y </span>
<span>y = (1/4) (x-1)^2 is the parabola</span>