I am totally stuck on this problem please help

How do you get the answer and sketch it to this graft

Katyanochek1 [597]

F(x) = -4(x - 2)² + 2
f(x) = -4((x - 2)(x - 2)) + 2
f(x) = -4(x² - 2x - 2x + 4) + 2
f(x) = -4(x² - 4x + 4) + 2
f(x) = -4(x²) + 4(4x) - 4(4) + 2
f(x) = -4x² + 16x - 16 + 2
f(x) = -4x² + 16x - 14
-4x² + 16x - 14 = 0
x = -16 +/- √(16² - 4(-4)(-14))
 2(-4)
x = -16 +/- √(256 - 224)
 -8
x = -16 +/- √(32)
 -8
x = -16 +/- 5.66
 -8
x = -16 + 5.66 x = -16 - 5.66
 -8 -8
x = -10.34 x = -21.66
 -8 -8
x = 1.2925 x = 2.7075
f(x) = -4x² + 16x - 14
f(1.2925) = -4(1.2925)² + 16(1.2925) - 14
f(1,2925) = -4(1.67055625) + 20.68 - 14
f(1.2925) = -6.682225 + 20.68 - 14
f(1.2925) = 13.997775 - 14
f(1.2925) = -0.002225
(x, f(x)) = (1.2925, -0.002225)
or
f(x) = -4x² + 16x - 14
f(2.7075) = -4(2.7075)² + 16(2.7075) - 14
f(2.7075) = -4(7.33055625) + 43.32 - 14
f(2.7075) = -29.322225 + 43.32 - 14
f(2.7075) = 13.997775 - 14
f(2.7075) = -0.002225
(x, f(x)) = (2.7075, -0.002225)
--------------------------------------------------------------------------------------------
f(x) = 2(x - 2)² + 1
f(x) = 2((x - 2)(x - 2)) + 1
f(x) = 2(x² - 2x - 2x + 4) + 1
f(x) = 2(x² - 4x + 4) + 1
f(x) = 2(x²) - 2(4x) + 2(4) + 1
f(x) = 2x² - 8x + 8 + 1
f(x) = 2x² - 8x + 9
2x² - 8x + 9 = 0
x = -(-8) +/- √((-8)² - 4(2)(9))
 2(2)
x = 8 +/- √(64 - 72)
 4
x = 8 +/- √(-8)
 4
x = 8 +/- √(8 × (-1))
 4
x = 8 +/- √(8)√(-1)
 4
x = 8 +/- 2.83i
 4
x = 2 +/- 1.415i
x = 2 + 1.415i x = 2 - 1.415i
f(x) = 2x² - 8x + 9
f(2 + 1.415i) = 2(2 + 1.415i)² - 8(2 + 1.415i) + 9
f(2 + 1.415i) = 2((2 + 1.415i)(2 + 1.415i)) - 16 - 11.32i + 9
f(2 + 1.415i) = 2(4 + 2.83i + 2.83i + 2.00225i²) - 16 - 11.32i + 9
f(2 + 1.415i) = 2(4 + 5.66i + 2.00225) - 16 - 11.32i + 9
f(2 + 1.415i) = 8 + 11.32i + 4.0045 - 16 - 11.32i + 9
f(2 + 1.415i) = 8 + 4.0045 - 16 + 9 + 11.32i - 11.32i
f(2 + 1.415i) = 12.0045 - 16 + 9
f(2 + 1.415i) = -3.9955 + 9
f(2 + 1.415i) = 5.0045
(x, f(x)) = (2 + 1.415i, 5.0045)
or
f(x) = 2x² - 8x + 9
f(2 - 1.415i) = 2(2 - 1.415i)² - 8(2 - 1.415i) + 9
f(2 - 1.415i) = 2((2 - 1.415i)(2 - 1.415i)) - 16 + 11.32i + 9
f(2 - 1.415i) = 2(4 - 2.83i - 2.83i + 2.00225i²) - 16 + 11.32i + 9
f(2 - 1.415i) = 2(4 - 5.66i + 2.00225) - 16 + 11.32i + 9
f(2 - 1.415i) = 8 - 11.32i + 4.0045 - 16 + 11.32i + 9
f(2 - 1.415i) = 8 + 4.0045 - 16 + 9 - 11.32i + 11.32i
f(2 - 1.415i) = 12.0045 - 16 + 9
f(2 - 1.145i) = -3.9955 + 9
f(2 - 1.415i) = 5.0045
(x, f(x)) = (2 - 1.415i, 5.0045)
--------------------------------------------------------------------------------------------
f(x) = -2(x - 4)² + 8
f(x) = -2((x - 4)(x - 4)) + 8
f(x) = -2(x² - 4x - 4x + 16) + 8
f(x) = -2(x² - 8x + 16) + 8
f(x) = -2(x²) + 2(8x) - 2(16) + 8
f(x) = -2x² + 16x - 32 + 8
f(x) = -2x² + 16x - 24
-2x² + 16x - 24 = 0
x = -16 +/- √(16² - 4(-2)(-24))
 2(-2)
x = -16 +/- √(256 - 192)
 -4
x = -16 +/- √(64)
 -4
x = -16 +/- 8
 -4
x = -16 + 8 x = -16 - 8
 -4 -4
x = -8 x = -24
 -4 -4
x = 2 x = 6
f(x) = -2x² + 16x - 24
f(2) = -2(2)² + 16(2) - 24
f(2) = -2(4) + 32 - 24
f(2) = -8 + 32 - 24
f(2) = 24 - 24
f(2) = 0
(x,f(x)) = (2, 0)
or
f(x) = -2x² + 16x - 24
f(6) = -2(6)² + 16(6) - 24
f(6) = -2(36) + 96 - 24
f(6) = -72 + 96 - 24
f(6) = 24 - 24
f(6) = 0
(x, f(x)) = (6, 0)

5 0

3 years ago

Mr.Brown is creating examples of systems of equations. He completes the steps to find the solution of the equation below. Based

julia-pushkina [17]

Answer:

infinitely many solutions

Step-by-step explanation:

0 = 0 ← is a true statement.

Indicates that the 2 lines are the same line, that is one lying on top of the other.

Thus the system has an infinite number of solutions

4 0

3 years ago

HELP I ONLY HAVE 2 MINUTES UNTIL MY TESTS ARE OVER -8 ≤ -1 True False

babunello [35]

Answer:

the answer is true

Step-by-step explanation:

the more you go negative the less it is so that's why -1 is greater than -8

6 0

3 years ago

Bhavik bought 3 liters of milk and 5 loaves of bread for a total of $11. A month later, he bought 4 liters of milk and 4 loaves

liberstina [14]

Answer:

the cost of a liter of milk is $0.75

the cost of a loaf of bread is $1.75

Step-by-step explanation:

Let

x------> the cost of a liter of milk

y------> the cost of a loaf of bread

we know that

------> equation A

------> equation B

Multiply equation A by

-------> equation C

Multiply equation B by

------> equation D

Adds equation C and equation D

Find the value of x

substitute the value of y in the equation A

4 0

3 years ago

Sisters Rosey and Valerie specialize in two different triathlon events. Rosey finds that her average cycling speed is 7 mph fast

Musya8 [376]

Valerie's running speed is 16 miles per hour.

6 0

3 years ago