12x - 18x^2
(Is that the form of answer they want?)
Y = -2(x - 1)² + 8
y = -2((x - 1)(x - 1)) + 8
y = -2(x² - x - x + 1) + 8
y = -2(x² - 2x + 1) + 8
y = -2(x²) + 2(2x) - 2(1) + 8
y = -2x² + 4x - 2 + 8
y = 2x² + 4x + 6
2x² + 4x + 6 = 0
x = <u>-4 +/- √(4² - 4(2)(6))</u>
2(2)
x = <u>-4 +/- √(16 - 48)</u>
4
x = <u>-4 +/- √(-32)
</u> 4<u>
</u>x = <u>-4 +/- 5.6568i
</u> 4
x = -4 +/- 1.4142i
x = -4 + 1.4142i x = -4 - 1.4142
y = -2x² + 4x + 6
y = -2(-4 + 1.4142i)² + 4(-4 + 1.4142i) + 6
y = -2((-4 + 1.4142i)(-4 + 4.4142i) - 16 + 5.6568i + 6
y = -2(16 - 5.6568i - 5.6568i + 1.99996164i²) - 16 + 5.6568i + 6
y = -2(16 - 11.3136i + 1.9996164) - 16 + 5.6568i + 6
y = -32 + 22.6272i - 3.99992328 - 16 + 5.6568i + 6
y = -32 - 3.99992328 - 16 + 6 + 22.6272i + 5.6568i
y = -35.99992328 - 16 + 6 + 28.284i
y = -51.99992328 + 6 + 28.284i
y = -45.99992328 + 28.284i
(x, y) = (-4 + 1.4142i, -45.99992328 + 28.284i)
y = -2x² + 4x + 6
y = -2(-4 - 1.4142i)² + 4(-4 - 1.4142i) + 6
y = -2((-4 - 1.4142i)(-4 - 1.4142i)) - 16 - 5.6568i + 6
y = -2(16 + 5.6568i + 5.6568i + 1.99996164i²) - 16 - 5.6568i + 6
y = -2(16 + 11.3136i + 1.99996164) - 16 - 5.6568i + 6
y = -32 - 22.6272i - 3.99992328 - 16 - 5.6568i + 6
y = -32 - 3.99992328 - 16 + 6 - 22.6272i - 5.6568i
y = -35.99992328 - 16 + 6 - 28.284i
y = -51.99992328 + 6 - 28.284i
y = -45.99992328 - 28.284i
(x, y) = (-4 - 1.4142i, -45.99992328 - 28.284i)
zeros: -4 + 1.4142i or -4 - 1.4142i
vertex: (-4 + 1.4142i, -45.99992328 + 28.284i) and (-4 - 1.4142i, -45.99992328 - 28.284i)
axis of symmetry: 0 + 2.8284i
<u />
9514 1404 393
Answer:
8. 4 +2q²/p² -4r/p +r²/p²
9. (x, y) = (3/4, -17/8)
Step-by-step explanation:
All of these questions are asking you to make use of the fact that ...
α + β = -q/p
αβ = r/p
__
8. (2 +α²)(2 +β²) = 4 + 2(α² +β²) +α²β²
= 4 +2((α+β)² -2αβ) +(αβ)²
Substituting the above for the sum and product, you have ...
= 4 + 2((-q/p)² -2(r/p)) +(r/p)²
= 4 +2q²/p² -4r/p +r²/p²
__
9. This is asking for the vertex of the parabola. The x-coordinate is ...
x=-b/(2a) = -(-3)/(2(2) = 3/4
Then the y-coordinate is ...
y = (2(3/4) -3)(3/4) -1 = (-3/2)(3/4) -1 = -9/8 -1 = -17/8
The (x, y) values of interest are (3/4, -17/8).
1 task per 12 mins. 5 tasks in 1 hour
Answer:
D: 128 fl. oz
Step-by-step explanation:
1 quart is 32, to multiply by 4. :D