Question

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

Answer 1

Given: $2x^2 - 12x + 1 = 0$

Step 1: $2(x^2- 6x + 3^2) + 1 - 2(3^2) = 0$

Step 2: $2(x^2 - 6x + 9) + 1 - 18 = 0$

Second answer:  $2(x - 3)^2 - 17 = 0$

Explanation in detail:

The quadratic equation a$x^{2} + bx + c = 0$'s vertex form is

where a$(x - h)^{2} + k$ equals zero

A is the $x^{2}$ coefficient, and h is the vertex's x-coordinate on the equation's graph.

The vertex of the equation's graph, k, has the y-coordinate.

The completing square can be used to determine the vertex form.

$2x^{2} - 12x + 1 = 0$ is the equation.

Put$2x^{2} -12x$ in a bracket and subtract 2 from them as a common component to utilize the completing square.

∵ $2(x^{2} - 6x) + 1 = 0$

To determine the product of the first and second terms in the binomial, divide the second term by two.

∵ $6x / 2 = 3x$

∵$3x = 3 * x$

∴ The binomial's first and second terms are x and 3, respectively.

The phrase in the bracket's middle is (-)

∴ Middle of the binomial's sign is (-)

∴ The binary value is $(x - 3)^2$

Square 3 is nine.

To keep the equation from altering, you must deduct the same number from the bracket after adding 9 there.

∴ $2(x^2 - 6x + 9 - 9) + 1 = 0$

- Remove the brace and multiply -9 by 2.

∵ $2 *-9 = -18$

∴ $2(x^2- 6x + 9) + 1 - 18 = 0$

- Construct a square binomial from $(x^{2} - 6x + 9)$

∵ $x^2 - 6x + 9 = (x - 3)^2$

∴ $2(x - 3)^2 + 1 - 18 = 0$

Include related terms.

∴$2(x - 3)^2 - 17 = 0$

∴ The equation's vertex form is$2(x - 3)^2 - 17 = 0.$

Given that: $2x^2 - 12x + 1 = 0$

Step 1: $2(x^2- 6x + 3^2) + 1 - 2(3^2) = 0$

Step 2: $2(x^2 - 6x + 9) + 1 - 18 = 0$

Step 3:  $2(x - 3)^2 - 17 = 0$

To know  more about the vertex form of quadratic equation visit:

https://brainly.com/question/14791174

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