Finding the vertex of a parabola from an equation

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.
  • #1
DLxX
58
0
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.
 
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  • #2
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:
  • #3
Plug in the point values to solve for k.

What kind of parabola is this? Sideways or vertical? (hint)
 
  • #4
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)?
 
  • #5
Show me the equation in the form of x =. Start from there. Did you solve for k?
 
  • #6
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?
 
  • #7
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?
 
  • #8
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.

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