Question

Y= - x^2 + 4x + 6 in vertex form

Answer 1

y = - (x - 2)² + 10

Step-by-step explanation:

the equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k ) are the coordinates of the vertex and a is a multiplier

To obtain this form use the method of completing the square

y = - x² + 4x + 6 ( factor out - 1 from the first 2 terms )

y = - (x² - 4x) + 6

To complete the square

add/subtract ( half the coefficient of the x- term )² to x² - 4x

y = - (x² + 2(- 2) + 4 - 4) + 6

y = - (x - 2)² + 4 + 6

y = - (x - 2)² + 10 ← in vertex form

Answer 2

HI THERE!

`\rm \color{lime}(2,10)`

step-by-step Step-by-step explanation:

`\rm \color{lime}y = - {x}^(2) + 4x + 6`

• identify the coefficients

`\rm \color{lime}a = - 1,b = 4`

• substitute the coefficient into the expression
• find the x-coordinate of the vertex by substituting a = - 1 and b=4
• 
  `\tt \tiny \: x = - (b)/(29)`

`\rm \color{lime}x = - (4)/(2x( - 1))`

• solve the equation for X
• find the y-coordinate of the vertex by evaluating the function for x = 2

`\rm \color{lime}y = - {x}^(2) + 4x + 6,x = 2`

• calculate the function value for x = 2

`\rm \color{lime}y = 10`

• since the value of the function is 10 for x = 2 the vertex of the graph of the quadratic function is a (2,10)

`= \rm \color{hotpink} (2,10)`

hope it helps