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The equation 2x2 − 12x + 1 = 0 is being rewritten in vertex form.
Fill in the missing step.
Given 2x2 − 12x + 1 = 0
Step 1 2(x2 − 6x ___) + 1 ___ = 0
Step 2 2(x2 − 6x + 9) + 1 − 18 = 0
Step 3 ✔

2(x − 3)2 + 17 = 0

2(x − 3)2 − 17 = 0

2(x + 3)2 − 17 = 0

2(x − 6)2 − 17 = 0

Respuesta :

Ashraf82

Given ⇒ 2x² - 12x + 1 = 0

Step 1 ⇒ 2(x² - 6x + 3²) + 1 - 2(3²) = 0

Step 2 ⇒ 2(x² - 6x + 9) + 1 - 18 = 0

Step 3 ⇒ 2(x - 3)² - 17 = 0 ⇒ 2nd answer

Step-by-step explanation:

The vertex form of the quadratic equation ax² + bx + c = 0 is

a(x - h)² + k = 0, where

  • a is the coefficient of x²
  • h is the x-coordinate of the vertex of the graph of the equation
  • k is the y-coordinate of the vertex of the graph of the equation

You can find the vertex form by using the completing square

∵ The equation is 2x² - 12x + 1 = 0

To use the completing square put 2x² - 12x in a bracket and take 2 from them as a common factor

∵ 2(x² - 6x) + 1 = 0

Divide the 2nd term by 2 to find the product of the 1st and 2nd terms of the binomial

∵ 6x ÷ 2 = 3x

∵ 3x = 3 × x

∴ The first term of the binomial is x and the second term is 3

∵ The middle term of the bracket is (-)

∴ The middle sign of the binomial is (-)

∴ The binomial is (x - 3)²

∵ Square 3 is 9

You must add 9 in the bracket, to keep the equation without changing you must subtract the same value

∴ 2(x² - 6x + 9 - 9) + 1 = 0

- Take -9 out the bracket and multiply it by 2

∵ 2 × -9 = -18

∴ 2(x² - 6x + 9) + 1 - 18 = 0

- Write (x² - 6x + 9) as a square binomial

∵ x² - 6x + 9 = (x - 3)²

∴ 2(x - 3)² + 1 - 18 = 0

Add the like terms

∴ 2(x - 3)² - 17 = 0

∴ The vertex form of the equation is 2(x - 3)² - 17 = 0

Given ⇒ 2x² - 12x + 1 = 0

Step 1 ⇒ 2(x² - 6x + 3²) + 1 - 2(3²) = 0

Step 2 ⇒ 2(x² - 6x + 9) + 1 - 18 = 0

Step 3 ⇒ 2(x - 3)² - 17 = 0

Learn more:

You can learn more about the vertex form of quadratic equation in brainly.com/question/9390381

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qwerty1128

Answer: Given ⇒ 2x² - 12x + 1 = 0

Step 1 ⇒ 2(x² - 6x + 3²) + 1 - 2(3²) = 0

Step 2 ⇒ 2(x² - 6x + 9) + 1 - 18 = 0

Step 3 ⇒ 2(x - 3)² - 17 = 0

The steps are

Separate the first two terms from the constant

Divide the coefficient of the x-term by 2, square the result, and add that inside the parenthesis to complete the square.

Since you added inside the parenthesis, you will need to subtract outside the parenthesis to keep the equation balanced.

Factor the trinomial inside the parenthesis and simplify the constant terms outside the parenthesis.

Do these steps to get B 2(x − 3)2 − 17 = 0

Step-by-step explanation:

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