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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