Find the Vertex of the Quadratic Function: y = (x + 14)² - 14

Q: Why is the x-coordinate -14 and not +14?

The vertex form is $ y = a(x - h)^2 + k $. Since we have $ (x + 14)^2 $, we must rewrite it as $ (x - (-14))^2 $. This means h = -14, not +14!

Q: How do I remember the vertex form pattern?

Remember: $ y = a(x - h)^2 + k $ has vertex $ (h, k) $. The opposite of what's with x gives you the x-coordinate, and k stays the same for the y-coordinate.

Q: What if the equation isn't in vertex form?

You'd need to complete the square first to convert it to vertex form. But this problem is already in vertex form, making it much easier to find the vertex directly!

Q: Can I check my answer by graphing?

Absolutely! The vertex $ (-14, -14) $ should be the lowest point of this parabola since it opens upward (positive coefficient). You can also substitute to verify the coordinates work.

Vertex Form with Standard Coordinate Identification

Find the vertex of the parabola

$y=(x+14)^2-14$

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Step-by-step video solution

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00:00 Find the vertex of the parabola

00:03 We will use the formula to describe the parabola function

00:10 The coordinates of the vertex are (P,K)

00:14 We will use this formula and find the vertex point

00:20 We notice that according to the formula, the term P is negative

00:26 We will substitute appropriate values according to the given data

00:33 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Find the vertex of the parabola

$y=(x+14)^2-14$

Step-by-step solution

To find the vertex of the parabola expressed by the equation $y = (x+14)^2 - 14$ , recognize that this is given in the vertex form of a quadratic equation:

The general vertex form of a quadratic equation is $y = a(x-h)^2 + k$ , where $(h, k)$ represents the vertex of the parabola.

In the given equation:

The $x$ term inside the parentheses is $x+14$ , which can be rewritten as $x - (-14)$ . This implies $h = -14$ .
The constant term outside the parentheses is $-14$ , which is the $k$ value indicating the vertical shift. Hence, $k = -14$ .

Therefore, the vertex of the parabola is determined by $(h, k) = (-14, -14)$ .

The solution to the problem is $(-14, -14)$ .

Final Answer

$(-14,-14)$

Key Points to Remember

Essential concepts to master this topic

Vertex Form: y = a(x - h)² + k has vertex (h, k)
Sign Rule: x + 14 becomes x - (-14), so h = -14
Check: Substitute x = -14: y = ((-14) + 14)² - 14 = 0 - 14 = -14 ✓

Common Mistakes

Avoid these frequent errors

Using the wrong sign for the h-coordinate
Don't use h = 14 from (x + 14)² = wrong vertex (14, -14)! The term (x + 14) means x - (-14), not x - 14. Always rewrite x + 14 as x - (-14) to correctly identify h = -14.

Practice Quiz

Test your knowledge with interactive questions

The following function has been graphed below:

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

Calculate point C.

FAQ

Everything you need to know about this question

Why is the x-coordinate -14 and not +14?

The vertex form is $y = a(x - h)^2 + k$ . Since we have $(x + 14)^2$ , we must rewrite it as $(x - (-14))^2$ . This means h = -14, not +14!

How do I remember the vertex form pattern?

Remember: $y = a(x - h)^2 + k$ has vertex $(h, k)$ . The opposite of what's with x gives you the x-coordinate, and k stays the same for the y-coordinate.

What if the equation isn't in vertex form?

You'd need to complete the square first to convert it to vertex form. But this problem is already in vertex form, making it much easier to find the vertex directly!

Can I check my answer by graphing?

Absolutely! The vertex $(-14, -14)$ should be the lowest point of this parabola since it opens upward (positive coefficient). You can also substitute to verify the coordinates work.

Why is this form better than standard form?

Vertex form immediately shows you the vertex location, while standard form $y = ax^2 + bx + c$ requires calculations or completing the square to find the vertex.

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Find the Vertex of the Quadratic Function: y = (x + 14)² - 14

Vertex Form with Standard Coordinate Identification

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why is the x-coordinate -14 and not +14?

How do I remember the vertex form pattern?

What if the equation isn't in vertex form?

Can I check my answer by graphing?

Why is this form better than standard form?

🌟 Unlock Your Math Potential

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