X=-8,3.
divide all terms by the two in the first term to get x^2+5x-24=0. Then find the factors. To do so, find what two numbers can be multiplied to get 24, and whether those two numbers can be added or subtracted to get the middle term (5). Since 8x(-3)=24 and 8-3=5, (x+8) and (x-3) are the factors. Then set the factors equal to zero. Add or subtract these numbers to the other side of the equation and you then get x=-8,3. These are the roots.
draw a perpendicular line from the directrix passing through the focus, this will be the line of symmetry.
The vertex(h, k) will be located on the line half way between the focus and directrix.
The distance from the focus to the vertex is called the focal length, call it a. The then equation is
(x - h)^2 = 4a(y - k)
the equation can be manipulated to
y = 1/4a(x - h)^2 + k
hope it helps
The GCF of 12, 21, and 30 is 3.
The factors of 12 are: 1, 2, 3, 4, 6, 12
<span>The factors of 21 are: 1, </span>3, 7, 21
<span>The factors of 30 are: 1, 2, </span>3, 5, 6, 10, 15, 30
<span>Then the greatest common factor is 3.
</span>
The GCF of 11, and 44 is 11.
The factors of 11 are: 1, 11
The factors of 44 are: 1, 2, 4, 11, 44
Then the greatest common factor is 11.
Hope this helps.
and simplifying:
, which is always true.