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How do you find the vertex of a parabola #y= [x-4]^2#?

Answer 1

Hazel Anglin

Find vertex

Vertex: x = 4 --> y = f(4) = 0

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Answer 2

Isaiah Anthony

The vertex is at #(4,0)#

#y=[x-4]^2# can be thought of as a variant of the vertex form for a parabolic equation: #color(white)("XXXX")##y = m(x-a)^2+b# with a vertex at #(a,b)#

Since #y=[x-4]^2# is equivalent to #y = 1(x-4)^2 + 0#

#color(white)("XXXX")#the vertex is at #(4,0)#

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Answer 3

Eva Abramson

To find the vertex of the parabola (y = (x - 4)^2), follow these steps:

Identify the values of (h) and (k) in the vertex form (y = (x - h)^2 + k). In this equation, (h) represents the x-coordinate of the vertex, and (k) represents the y-coordinate of the vertex.
For the given equation (y = (x - 4)^2), the value of (h) is 4 because (x - h = x - 4), so (h = 4).
Since there is no constant term added or subtracted outside the squared term, (k = 0).
Therefore, the vertex of the parabola is at the point ((4, 0)).

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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.