Respuesta :

HI THERE!

[tex] \rm \color{lime}(2,10)[/tex]

step-by-step explanation:

[tex]\rm \color{lime}y = - {x}^{2} + 4x + 6[/tex]

  • identify the coefficients

[tex]\rm \color{lime}a = - 1,b = 4[/tex]

  • substitute the coefficient into the expression
  • find the x-coordinate of the vertex by substituting a = - 1 and b=4
  • [tex] \tt \tiny \: x = - \frac{b}{29} [/tex]

[tex]\rm \color{lime}x = - \frac{4}{2x( - 1)} [/tex]

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

[tex]\rm \color{lime}y = - {x}^{2} + 4x + 6,x = 2[/tex]

  • calculate the function value for x = 2

[tex]\rm \color{lime}y = 10[/tex]

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

[tex] = \rm \color{hotpink} (2,10)[/tex]

hope it helps

Answer:

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

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