Question

Which equation is y = −6x² + 3x + 2 rewritten in vertex form?

a. −6(x-1)² + 8
b. -6(x+1/4)² + 13/8
c. y = -6(x-1/4)² + 19/8
d. y = -6(x-1/2)² + 7/2

Answer 1

To convert the given quadratic equation into vertex form, we complete the square for the expression y = -6x² + 3x + 2 and find the correct vertex form to be y = -6(x-1/4)² + 19/8.

Step-by-step explanation:

The student's question is about rewriting the quadratic equation y = −6x² + 3x + 2 into vertex form. To do this, we utilize the process of completing the square:

• 
  
• First, factor out the coefficient of the x² term from the x-terms of the quadratic expression, which in this case is -6.
• 
  
• The equation becomes y = -6(x² - ⅓x) + 2. Now we need to find a value that completes the square for the expression x² - ⅓x.
• 
  
• The value to complete the square is (-⅓/2)² = (-3/4)² = 9/16, which is then factored into the equation as follows: y = -6[(x - 1/4)² - 9/16] + 2.
• 
  
• To get the vertex form, we distribute the -6 inside the bracket and then add the constant outside to find the final equation.
• 
  
• After simplifying the constants, the vertex form of the equation is y = -6(x-1/4)² + 19/8.

So, the correct choice that represents the vertex form of the quadratic equation y = -6x² + 3x + 2 is c. y = -6(x-1/4)² + 19/8.