Discover the Vertex of the Parabola: Analyzing y = (x-7) - 7

Find the vertex of the parabola

y=(x7)7 y=(x-7)-7

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find the vertex of the parabola
00:03 Use the formula to describe the parabolic function
00:09 The coordinates of the vertex are (P,K)
00:15 Use this formula and find the vertex point
00:22 Substitute appropriate values according to the given data
00:26 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

Find the vertex of the parabola

y=(x7)7 y=(x-7)-7

2

Step-by-step solution

The given equation is y=(x7)7 y = (x-7) - 7 .

First, simplify the equation:
y=x77=x14 y = x - 7 - 7 = x - 14 .

This is a linear equation in the form y=x14 y = x - 14 . However, since the problem asks about a vertex, there might be a reconsideration needed if a quadratic term is missing. Since the question specifies a parabola, let's convert back:

Let's convert this into a complete square form:

Express y=(x7)27 y = (x - 7)^2 - 7 , assuming we meant to represent:
y=(xh)2+k y = (x-h)^2 + k

The vertex form representation would look like:
y=(x7)2+(7) y = (x-7)^2 + (-7)

Hence, the vertex is (7,7)(7, -7).

Therefore, the vertex of the parabola is (7,7)(7, -7).

3

Final Answer

(7,7) (7,-7)

Practice Quiz

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Find the standard representation of the following function:

\( f(x)=(x-3)^2+x \)

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