Home > Algebra > Vertex Form of a Quadratic Equation

How do you find the vertex given #y=x^2 -4#?

Answer 1

The Vertex is (0,-4)

graph{x^2-4[-5, 5, 10, 10]}

While there are several methods for obtaining the vertex, graphing is the most time-consuming, as demonstrated above.

If you are into formulas, you can remember #(y-k)=(x-h)^2#, where the vertex is #(h,k)#. This formula is easily derivable, and you can probably find a proof for it in Wikipedia.

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Answer 2

Genesis Allen

To find the vertex of the quadratic function ( y = x^2 - 4 ), use the formula ( x = -\frac{b}{2a} ), where ( a ) and ( b ) are the coefficients of the quadratic equation. In this case, ( a = 1 ) and ( b = 0 ). Substituting these values into the formula, you get ( x = -\frac{0}{2(1)} = 0 ). Then, substitute ( x = 0 ) into the original equation to find the corresponding ( y )-value. So, ( y = (0)^2 - 4 = -4 ). Therefore, the vertex is at ( (0, -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.