# Finding the vertex of a parabola from an equation

• DLxX
In summary, the parabola y^2 - x + 4y + k = 0 passes through the point (12,1) and to find the vertex, you need to plug in the values of x and y and then complete the square to put it in the form f(y) = x = (y+a)^2+b. The vertex coordinates can be found by taking the values of b and -a.
DLxX
I need help with the following question.

The parabola y^2 - x + 4y + k = 0 passes through the point (12,1). Find the vertex of the parabola.

DLxX said:
I need help with the following question.

The parabola y^2 - x + 4y + k = 0 passes through the point (12,1). Find the vertex of the parabola.

by differentiating ? or the line of symmetry between the roots of the equation ?

or completin the square ?

Last edited:
Plug in the point values to solve for k.

What kind of parabola is this? Sideways or vertical? (hint)

Jameson said:
Plug in the point values to solve for k.

What kind of parabola is this? Sideways or vertical? (hint)
would be a sideways since the y is squared, but how would i find the h in (h,k)?

Show me the equation in the form of x =. Start from there. Did you solve for k?

Jameson said:
Show me the equation in the form of x =. Start from there. Did you solve for k?
x = y^2 + 4y + k. So to solve for k do I then plug in 12 and 1 for x and y?

DeathKnight said:
Yup that's what you have to do.
Alright so that would give me the k value, but what about the h value?

DLxX said:
I need help with the following question.

The parabola y^2 - x + 4y + k = 0 passes through the point (12,1). Find the vertex of the parabola.
plug in values , then just complete the square to put it in the form

f(y) = x = (y+a)^2+b

and b,-a is the vertex

## What is the vertex of a parabola?

The vertex of a parabola is the point where the parabola reaches its maximum or minimum value. It is also known as the "turning point" of the parabola.

## How do you find the vertex of a parabola from its equation?

To find the vertex of a parabola from its equation, you can use the formula x = -b/2a, where a and b are the coefficients of the quadratic equation in the form of ax^2 + bx + c. Substituting the value of x in the equation will give you the y-coordinate of the vertex.

## Can you find the vertex of a parabola if the equation is not in standard form?

Yes, you can still find the vertex of a parabola if the equation is not in standard form. You can use the process of completing the square to convert the equation into standard form and then use the formula x = -b/2a to find the vertex.

## What does the a coefficient in a quadratic equation represent?

The a coefficient in a quadratic equation represents the coefficient of the x^2 term. It determines the shape of the parabola and whether it opens upwards or downwards.

## Is the vertex always the highest or lowest point on a parabola?

Yes, the vertex is always the highest or lowest point on a parabola. If the parabola opens upwards, the vertex will be the minimum point, and if it opens downwards, the vertex will be the maximum point.

• General Math
Replies
44
Views
3K
• General Math
Replies
7
Views
3K
• General Math
Replies
4
Views
1K
• General Math
Replies
4
Views
1K
• General Math
Replies
1
Views
934
• General Math
Replies
4
Views
3K
• General Math
Replies
6
Views
1K
• General Math
Replies
5
Views
2K
• Calculus and Beyond Homework Help
Replies
12
Views
1K
• General Math
Replies
4
Views
30K