How do find the vertex and axis of symmetry for a quadratic equation #y=-2x^2-8x+3#?
See the explanation below.
graph{y=-2x^2-8x+3 [-16.42, 15.6, -3.2, 12.82]}
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To find the vertex and axis of symmetry for the quadratic equation ( y = -2x^2 - 8x + 3 ), follow these steps:
- Write the equation in vertex form: ( y = a(x - h)^2 + k ), where ( (h, k) ) represents the vertex.
- Complete the square to rewrite the equation in vertex form.
- 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:
- Start with the given equation: ( y = -2x^2 - 8x + 3 ).
- Rewrite the equation by factoring out the common factor ( -2 ) from the ( x^2 ) and ( x ) terms: ( y = -2(x^2 + 4x) + 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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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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