Jada made 6 cups of blueberry jam and divided the Jam in 4 containers. How much jam went in each container
1 answer:
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Answer:
x = y²
Step-by-step explanation:
Any point (x, y ) on the parabola is equidistant from the focus and the directrix
Using the distance formula, then
= | x + 3 |
Squaring both sides
(x - 3)² + y² = (x + 3)² ← expanding both sides
x² - 6x + 9 + y² = x² + 6x + 9 ← subtract x² + 6x + 9 from both sides
- 12x + y² = 0 ( subtract y² from both sides )
- 12x = - y² ( divide both sides by - 12 )
x = y²
Synthetic division is used since the equation is of the third degree. The divisors of -3 are 1, -1, 3, +3. So:
| 2 -7 8 -3
<u>1 | 2 -5 3</u>
| 2 -5 3 0
<u> 1 | 2 -3 </u>
2 -3 0
So the factorization is (x-1)² (2x-3)=0. So:
Synthetic division is used since the equation is of the third degree. The divisors of -4 are 1, -1, 2, -2, 4, -4. So:
| 1 -1 0 -4
<u>2 | 2 2 </u>
1 2 2 0
So the factorization is (x-2)(x²+x+2)=0 . When calculating the discriminant of the trinomial, it is concluded that it has no roots since the result is negative. So you only have one solution.
Synthetic division is used since the equation is of the third degree. The divisors of 2 are 1, -1, 2, -2. So:
| 6 7 9 2
<u>-2 | -12 10 -2</u>
6 -5 1 0
So the factorization is (x+2)(6x²-5x+1)=0 . The quadratic equation is solved by the general formula: