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>
Answer:
slope=-9/2
y int- 6
Step-by-step explanation:
okay lets take two points
-2,15 and -6,33
the slope is 33-15/ -6-(-2)= 18/-4=-9/2
equation is y=mx+b where m is slope and b is y intercept
so plugging values in we get
15=-2(-9/2)+b
15=9+b
b=6
Answer:
The numbers are x = 3 and y = 1. Therefore the value of xy is 3.
Step-by-step explanation:
In order to calculate the numbers we will simplify the equation, this is done bellow:
2*x + x(2^2) + (y*2^3) + (y*2^4) = 42
2*x + 4*x + 8*y + 16*y = 42
6*x + 24*y = 42
We can divide the whole equation by 6, so we have:
x + 4*y = 7
The only possible combination of numbers that are positive and integers that will make the equation valid is x = 3 and y = 1. Therefore he value of xy is 3.