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There are two forms in which a quadratic equation can be written: general form, which is ax2 + bx + c, and standard form, which is a(x - q)2 + p. In standard form, the vertex is (q, p). So to find the vertex, simply convert general form into standard form.

The formula often used to convert between these two forms is:

ax2 + bx + c = a(x + b/2a)2 + c - b2/4a

Substitute the variables:

-2x2 + 12x - 13 = -2(x + 12/-4)2 -13 + 122/-8

-2x2 + 12x - 13 = -2(x - 3)2 + 5

Since the co-ordinates of the vertex are equal to (q, p), the vertex of the parabola defined by the equation y = -2x2 + 12x - 13 is located at point (3, 5)

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Q: What is the vertex of the parabola y equals -2x squared plus 12x -13?
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What is the vertex for the parabola y equals x squared plus 4x plus 5?

The vertex of a parabola is the minimum or maximum value of the parabola. To find the maximum/minimum of a parabola complete the square: x² + 4x + 5 = x² + 4x + 4 - 4 + 5 = (x² + 4x + 4) + (-4 + 5) = (x + 2)² + 1 As (x + 2)² is greater than or equal to 0, the minimum value (vertex) occurs when this is zero, ie (x + 2)² = 0 → x + 2 = 0 → x = -2 As (x + 2)² = 0, the minimum value is 0 + 1 = 1. Thus the vertex of the parabola is at (-2, 1).


What is x squared minus 8x plus 8y plus 32 equals 0 in standard parabola form?

7


How do you find the axis of symmetry and vertex of y equals x squared plus 6x plus 10?

By completing the square y = (x+3)2+1 Axis of symmetry and vertex: x = -3 and (-3, 1) Note that the parabola has no x intercepts because the discriminant is less than zero


What is the vertex of a parabola whose equation is y equals x 32?

The given equation is not that of a parabola since there are no powers of 2. Unfortunately, limitations of the browser used by Answers.com means that we cannot see most symbols. It is therefore impossible to give a proper answer to your question. Please resubmit your question spelling out the symbols as "plus", "minus", "equals" etc. And using ^ to indicate powers (eg x-squared = x^2).


What are points of intersection of the line 3x -y equals 5 with the curve of 2x squared plus y squared equals 129?

Straight line: 3x-y = 5 Curved parabola: 2x^2 +y^2 = 129 Points of intersection works out as: (52/11, 101/11) and (-2, -11)

Related questions

What is the vertex of the parabola y equals 2x squared plus 12x 13?

(-3, -5)


What is the vertex of the parabola when y equals 3x squared plus 2x minus 1?

The minimum value of the parabola is at the point (-1/3, -4/3)


What is the vertex of the parabola y equals x2 plus 8x plus 5?

The vertex has a minimum value of (-4, -11)


What is Y equals x squared plus 1?

It is the equation of a parabola.


What is the vertex form of y equals x2 plus 4x - 7?

The vertex of the positive parabola turns at point (-2, -11)


What is the vertex of the function y equals x squared plus 4?

The vertex is at the point (0, 4).


What is the vertex of the parabola given by the equation x equals negative 4 times y minus 3 squared plus 2?

Question can be taken as multiple meanings. Please see discussion.


How does y equals 4x2 plus 21x look in a graph?

It is a parabola with its vertex at the origin and the arms going upwards.


What is the vertex for the parabola y equals x squared plus 4x plus 5?

The vertex of a parabola is the minimum or maximum value of the parabola. To find the maximum/minimum of a parabola complete the square: x² + 4x + 5 = x² + 4x + 4 - 4 + 5 = (x² + 4x + 4) + (-4 + 5) = (x + 2)² + 1 As (x + 2)² is greater than or equal to 0, the minimum value (vertex) occurs when this is zero, ie (x + 2)² = 0 → x + 2 = 0 → x = -2 As (x + 2)² = 0, the minimum value is 0 + 1 = 1. Thus the vertex of the parabola is at (-2, 1).


What is x squared minus 8x plus 8y plus 32 equals 0 in standard parabola form?

7


What is the y value of the maximum y equals -x2 plus 6x-7?

20 and the vertex of the parabola is at (3, 20)


How do you find the axis of symmetry and vertex of y equals x squared plus 6x plus 10?

By completing the square y = (x+3)2+1 Axis of symmetry and vertex: x = -3 and (-3, 1) Note that the parabola has no x intercepts because the discriminant is less than zero