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

Vertex Form with Missing Squared Terms

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

Follow each step carefully to understand the complete solution
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)

Key Points to Remember

Essential concepts to master this topic
  • Vertex Form: Standard format is y=(xh)2+k y = (x-h)^2 + k with vertex (h,k)
  • Technique: Convert y=(x7)7 y = (x-7) - 7 to y=(x7)27 y = (x-7)^2 - 7 assuming parabola
  • Check: Vertex (7,-7) makes y=(77)27=07=7 y = (7-7)^2 - 7 = 0 - 7 = -7

Common Mistakes

Avoid these frequent errors
  • Treating linear equations as parabolas
    Don't assume y=(x7)7 y = (x-7) - 7 is a parabola without the squared term = no vertex exists! Linear equations are straight lines, not curves. Always check if the equation has an x2 x^2 term before finding a vertex.

Practice Quiz

Test your knowledge with interactive questions

The following function has been graphed below:

\( f(x)=x^2-6x \)

Calculate point C.

CCCAAABBB

FAQ

Everything you need to know about this question

How can I tell if an equation represents a parabola?

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A parabola must have an x2 x^2 term! If you only see x x (not x2 x^2 ), it's a straight line, not a parabola.

What if the problem says 'parabola' but I don't see x²?

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There might be a typo in the problem. The most likely intended equation is y=(x7)27 y = (x-7)^2 - 7 , which gives vertex (7, -7).

How do I find the vertex from vertex form?

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In y=(xh)2+k y = (x-h)^2 + k , the vertex is simply (h, k). For y=(x7)27 y = (x-7)^2 - 7 , that's (7, -7)!

Why is the vertex (7, -7) and not (-7, 7)?

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Be careful with signs! In y=(x7)27 y = (x-7)^2 - 7 , we have h = 7 (positive) and k = -7 (negative), giving vertex (7, -7).

What does the vertex tell me about the parabola?

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The vertex is the turning point - either the highest or lowest point on the parabola. Since our coefficient of x2 x^2 is positive, (7, -7) is the minimum point.

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