Respuesta :

johnny837

Answer:

(2, -32)

Step-by-step explanation:

1) Expand them.

y = 2(x² - 6x + 2x - 12)

y = 2(x² - 4x - 12)

y = 2x² - 8x - 24.

2) Complete the square to find the vertex.

y = 2([x² - 4x)] - 24

y = 2[(x - 2)² - 4] - 24

y = 2(x - 2)² - 8 - 24

y = 2(x - 2)² - 32

The vertex: (2, -32)

or you can use this: x = -b/2a

x = -(-8)/2(2)

x = 8/4

x = 2

Substitute the value into the original equation for y.

y = 2(2)² - 8(2) - 24

y = 2(4) - 16 - 24

y = 8 - 16 - 24

y = -32

Vertex: (2, -32)

sqdancefan

Answer:

  (2, -32)

Step-by-step explanation:

The vertex of the graph of a quadratic equation is on the line of symmetry, halfway between the x-intercepts. It can be found by evaluating the equation at that point.

Line of symmetry

The given function is written in factored form, so the x-intercepts are easy to find. They are the values of x that make the factors zero:

  (x +2) = 0   ⇒   x = -2

  (x -6) = 0   ⇒   x = 6

The midpoint between these values of x is their average:

  x = (-2 +6)/2 = 4/2

Then the x-coordinate of the vertex, and the equation of the line of symmetry is ...

  x = 2

Vertex

Using this value of x in the quadratic relation, we find the y-value at the vertex to be ...

  y = 2(2 +2)(2 -6) = 2(4)(-4)

  y = -32

The coordinates of the vertex are (x, y) = (2, -32).

Ver imagen sqdancefan

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