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How do you find the vertex of a parabola #g(x)=x^2+2x-3#?

Answer 1

Genesis Allen

Find vertex of g(x) = x^2 + 2x - 3

x-coordinate of vertex: x = (-b/2a) = -2/2 = - 1

y-coordinate of vertex: y = f(-1) = 1 - 2 + 3 = 2

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Answer 2

Isaiah Anthony

To find the vertex of a parabola represented by the equation ( g(x) = x^2 + 2x - 3 ), you can use the formula for the x-coordinate of the vertex, which is given by ( x = \frac{-b}{2a} ), where ( a ) is the coefficient of ( x^2 ) and ( b ) is the coefficient of ( x ) in the quadratic equation ( ax^2 + bx + c ). Plugging the values of ( a ) and ( b ) from the equation ( g(x) ), you get ( a = 1 ) and ( b = 2 ). Substituting these values into the formula, you get ( x = \frac{-2}{2 \times 1} = -1 ). To find the corresponding y-coordinate, substitute ( x = -1 ) into the equation ( g(x) ), which gives ( g(-1) = (-1)^2 + 2(-1) - 3 = 1 - 2 - 3 = -4 ). So, the vertex of the parabola is ( (-1, -4) ).

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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.