How do find the vertex and axis of symmetry for a quadratic equation #y=-2x^2-8x+3#?

Answer 1

See the explanation below.

General equation for the quadratic formula: #y=ax^2+bx+c#
The graph of a quadratic equation is a parabola.The axis of symmetry is the vertical line that separates the parabola into two equal halves.The point on the x-axis where the vertical axis is placed is determined by the formula #x=(-b)/(2a)#
#y=ax^2+bx+c#
#y=-2x^2-8x+3#
#a=-2# and #b=-8#
#x=(-(-8))/(2(-2))=8/-4=-2#
#x=-2#
Substitute #-2# for #x# into the equation to find #y#.
#y=-2(-2)^2-8(-2)+3#
#y=-2(4)+16+3#
#y=-8+16+3=11#
#y=11#
The vertex of a parabola is the point where the parabola crosses its axis of symmetry. Vertex#=##(x,y)=(-2,11)#

graph{y=-2x^2-8x+3 [-16.42, 15.6, -3.2, 12.82]}

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Answer 2

To find the vertex and axis of symmetry for the quadratic equation ( y = -2x^2 - 8x + 3 ), follow these steps:

  1. Write the equation in vertex form: ( y = a(x - h)^2 + k ), where ( (h, k) ) represents the vertex.
  2. Complete the square to rewrite the equation in vertex form.
  3. Once in vertex form, the vertex is at ( (h, k) ), and the axis of symmetry is the vertical line ( x = h ).

Now, let's apply these steps to the given equation:

  1. Start with the given equation: ( y = -2x^2 - 8x + 3 ).
  2. Rewrite the equation by factoring out the common factor ( -2 ) from the ( x^2 ) and ( x ) terms: ( y = -2(x^2 + 4x) + 3 ).
  3. Complete the square inside the parentheses: [ y = -2(x^2 + 4x + 4 - 4) + 3 ] [ y = -2[(x + 2)^2 - 4] + 3 ] [ y = -2(x + 2)^2 + 8 + 3 ] [ y = -2(x + 2)^2 + 11 ]

Now, the equation is in vertex form ( y = a(x - h)^2 + k ), where ( (h, k) = (-2, 11) ).

So, the vertex is at ( (-2, 11) ), and the axis of symmetry is the vertical line ( x = -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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