Question

Write 2x^2+12x+3=0 in vertex form?

Answer 1

Answer:

y = 2x^2+12x+3 = 2(x + 3)^2 - 15

Step-by-step explanation:

• Take 2 as a common factor out of the first 2 terms
• 2(x^2 + 6x) + 3 = 0

• Add half 6 squared inside the brackets. Subtract the same number outside the brackets when multiplied by 2
• 2(x^2 + 6x + 3^2) + 3 - 2*3^2 = 0

• Combine the two terms on the end.
• 2(x^2 + 6x + 9) + 3 - 2*9 = 0
• 2(x^2 + 6x + 9) + 3 - 18 = 0
• 2(x^2 + 6x + 9)  - 15 = 0

• Express the terms inside the brackets as a perfect square
• 2(x + 3)^2 - 15 = 0

Discussion Graph

Technically, the vertex form would y = 2(x + 3)^2 - 15. It needs to be more general than equated to zero. I have solved it the way you presented it and graphed it by definition.

• The red graph is y = 2x^2 + 12x + 3
• The blue graph is y = 2(x + 3)^2 - 15

Notice they have the same critical point which means they are equivalent