Question

Rewrite the function by completing the square. f(x)= 2 x^{2} +13 x +20f(x)=2x 2 +13x+20f, left parenthesis, x, right parenthesis, equals, 2, x, squared, plus, 13, x, plus, 20 f(x)=f(x)=f, left parenthesis, x, right parenthesis, equals (x+(x+left parenthesis, x, plus )^2+) 2 +right parenthesis, squared, plus

Answer 1

`f(x)=2\left(x+(13)/(4)\right)^2-(9)/(8)`

Explanation:

Given function:

`f(x)=2x^2+13x+20`

Factor out 2 from the terms in x:

`f(x)=2\left(x^2+(13)/(2)x\right)+20`

Add the square of half the coefficient of x inside the parentheses, and subtract the distributed equivalent outside the parentheses:

`f(x)=2\left(x^2+(13)/(2)x+\left(((13)/(2))/(2)\right)^2\right)+20-2\left(((13)/(2))/(2)\right)^2`

Simplify:

`f(x)=2\left(x^2+(13)/(2)x+\left((13)/(4)\right)^2\right)+20-2\left((13)/(4)\right)^2`

`f(x)=2\left(x^2+(13)/(2)x+(169)/(16)\right)+20-(169)/(8)`

`f(x)=2\left(x^2+(13)/(2)x+(169)/(16)\right)-(9)/(8)`

Factor the perfect trinomial inside the parentheses:

`f(x)=2\left(x+(13)/(4)\right)^2-(9)/(8)`

Answer 2

• f(x) = 2(x + 13/4)² - 9/8

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Given

• Function f(x) = 2x² + 13x + 20

Rewrite it by completing the square

• f(x) =
• 2x² + 13x + 20 =
• 2(x² + 13/2 x) + 20 =
• 2[x² + 2x*13/4 + (13/4)² - (13/4)²] + 20 =
• 2(x + 13/4)² - 169/8 + 20 =
• 2(x + 13/4)² - (169 - 8*20)/8 =
• 2(x + 13/4)² - 9/8