Answer:
<em>The equation of the Parabola</em>
<em>(y - 6 )² = 8 (x -6)</em>
Step-by-step explanation:
<u><em>Step(i):-</em></u>
Given directrix x = 4
we know that x = h - a = 4
h -a = 4 ...(i)
Given Focus = ( 8,6)
we know that the Focus of the Parabola
( h + a , k ) = ( 8,6)
comparing h + a = 8 ...(ii)
k = 6
solving (i) and (ii) and adding
h - a + h+ a = 8 +4
2 h = 12
h =6
Put h = 6 in equation (i)
⇒ h - a =4
⇒ 6 - 4 = a
⇒ a = 2
<u><em>Step(ii):-</em></u>
<em>The equation of the Parabola ( h,k) = (6 , 6)</em>
<em>( y - k )² = 4 a ( x - h )</em>
<em>(y - 6 )² = 4 (2) (x -6)</em>
<em>(y - 6 )² = 8 (x -6)</em>
<u><em></em></u>
Answer:
Vertex = (-3, -1)
Axis of Symmetry: x = -3
Step-by-step explanation:
The vertex is (-3, -1), the axis of symmetry is x = -3. The x-intercept is -2 and -4, the y intercept is 8, the domain is R, the range is [-1, inf.]
The function is increasing in {-3, inf.} and decreasing in {-inf., 3}
Answer:5/10
Step-by-step explanation:
1/2 x 5 = 5/10
First you have to factor (aka, multiply) your binomial (which is what you have written) usually it helps to organize your thinking, and help tell what you need to multiply, to use the binomial chicken(or crab claw, what ever you want to call it) which basically you draw two arches, one arch connecting the 3 and 4, and then the other the 3 and 9i. on the opposite side (depending on wheater you connected then from the top or bottom) you connect (with an arch) the 6i and the four, and then the 6i to the 9i.
so now you multiply each piece you've connected:
3 x 4= 12
3 x 9i= 27i
6i x 4= 24i
6i x 9i= 54i^2
after you've done this you can move on to putting it into standard form, which just means you put things in descending order, depending on how many exponents the x (or in this case i) has.
your largest exponent is 54i^2, so that's first in out equation, next 27i, and 24i (you can combine these because they are like term) which equals 51i, after that you just add the 12 on the end, so the final equation looks like this:
54i^2+51i+12
