Can some please help me with this question? And can you show your work too? I will mark the best answer Brainliest

Finding the vertex by completing the square

1) The vertex = (4/3, -4/3)

2) The vertex = (-1/2, 36)

3) The vertex = (2/3, 26/3)

Finding the value of x by completing the square

1) x = 1 or -4

2) x = 3/2 or -7/2

3) x = 1 or -3

Step-by-step explanation:

Finding the vertex by completing the square

The vertex form of the quadratic equation y = ax² + bx + c is written as follows;

y = a(x - h) + k

Therefore, we have;

Y = 3·x² + 4 - 8·x = a(x - h)² + k

Hence, a  = 3

Which gives;

3×(x² - 2·x·h + h²) + k

Hence, we have 3×2×h = 8

h = 8/6 = 4/3

The constant term = k

We note that 3 × h² + k = 4

∴ k = 4 - 16/3 = -4/3

The vertex form is therefore;

Y = 3(x - 4/3)² - 4/3

The vertex = (4/3, -4/3)

2) Where Y = 4·x² + 4·x + 36

a = 4

4× -2·h = 4

∴ h = 4/(4 × (-2)) = 4/-8 = -1/2

Also, 4 × h² + k = 36

Which gives;

4 × (-1/2)² × k = 36

k = 36

The vertex form becomes

y = 4(x - (-1/2)) + 36

The vertex = (-1/2, 36)

3) Where Y = -3·x² + 4·x + 10, we have

a = -3

3×2×h = 4

∴ h = 4/(2×3) = 2/3

a×h² + c = k

-(3)×(2/3)² + 10 =  26/3

Which gives;

Y = -3(x - 2/3) + 26/3

The vertex = (2/3, 26/3)

To find the value of x by completing the square, we have;

1) 2·x² = -6·x + 8

2·x² + 6·x =  8

2·(x² + 3·x) = 8

x² + 3·x = 8/2 = 4

x² + 3·x + (3/2)² = 4 + (3/2)² = 25/4

(x + 3/2)² = 25/4

∴ x + 3/2 = ±5/2

x = 5/2 - 3/2 or -5/2 - 3/2

x = 1 or -4

2) 8·x² + 16·x = 42

8·(x² + 2·x) = 42

x² + 2·x = 42/8 = 21/4

x² + 2·x + 1 = 21/4 + 1 = 25/4

(x + 1)² = 25/4

x + 1 = √(25/4) = ± 5/2

x = 5/2 - 1 or -5/2 - 1

∴ x = 3/2 or -7/2

3) -x² + 2·x = -3

-x² + 2·x = -3

-1×(-x² + 2·x) = -1 ×-3 = 3

x² - 2·x = 3

x² - 2·x + 1 = 3 + 1 = 4

(x - 1)² = 4

x - 1 = √4 = ±2

∴ x = 2 - 1 or -2 - 1

x = 1 or -3

-8

step-by-step explanation: