How do you find the vertex of #y=x^2 + 4x + 2#?

Answer 1

Convert the given equation into vertex form to find:
vertex at #(-2,-2)#

The general vertex form for a parabola is #color(white)("XXX")y=m(x-color(red)(a))^2+color(blue)(b)# with its vertex at #(color(red)(a),color(blue)(b))#
Given #color(white)("XXX")y=x^2+4x+2# Completing the square #color(white)("XXX")y=x^2+4xcolor(green)(+4)+2color(green)(-4)#
#color(white)("XXX")y=(x+2)^2-2#
#color(white)("XXX")y=(x-(color(red)(-2)))^2+(color(blue)(-2))#
which is in vertex form with the vertex at #(color(red)(-2),color(blue)(-2))#
Just to help verify this result, here is the graph of #y=x^2+4x+2#: graph{x^2+4x+2 [-8.702, 2.397, -3.11, 2.437]}
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Answer 2

To find the vertex of the quadratic function ( y = x^2 + 4x + 2 ), follow these steps:

  1. Identify the coefficients ( a ), ( b ), and ( c ) in the quadratic equation ( y = ax^2 + bx + c ).
  2. Use the formula ( x = \frac{{-b}}{{2a}} ) to find the x-coordinate of the vertex.
  3. Substitute the x-coordinate obtained in step 2 into the original equation to find the y-coordinate of the vertex.
  4. The coordinates of the vertex are ((x, y)).

Using the given equation ( y = x^2 + 4x + 2 ):

  1. ( a = 1 ), ( b = 4 ), and ( c = 2 ).
  2. ( x = \frac{{-4}}{{2(1)}} = -2 ).
  3. Substitute ( x = -2 ) into the equation: ( y = (-2)^2 + 4(-2) + 2 = 4 - 8 + 2 = -2 ).
  4. The vertex is at ((-2, -2)).
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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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