0
The vertex of the parabola below is at the point 3 25 and the point 4 55 is on the parabola What is the equation of the parabola?
Let the polynomial be y = ax^2 + bx + c
The derivative or slope at the minimum is zero: 2ax + b = 0
We have 55 = a (4^2) + b (4) + c
25 = a (3^2) + b (3) + c
and 2a(3) + b = 0 or b = -6a
55 = 16a - 24a + c = -6a + c
25 = 9a -18a +c = - 9a + c
30 = 3a
a = 10
b = -60
c = 55 + 6a = 115
The parabola is y = 10x^2 - 60x + 115
Check using, for instance
http://www.wolframalpha.com/input/?i=evaluate+y+%3D+10x^2+-+60x+%2B+115+at+x%3D3
and
http://www.wolframalpha.com/input/?i=minimize++10x^2+-+60x+%2B+115
Add your answer:
Earn +20 pts
What does vertex mean in math class?
A vertex is the highest or lowest point in a parabola.
The vertex of the parabola below is at the point 1 3 and the point 4 4 is on the parabola What is the equation of the parabola?
(y - 3) = a(x - 1)2 y = a(x - 1)2 + 3 4 = a(4 - 1)2 + 3 1 = 9a a = 1/9 y = 1/9 (x - 1)2 + 3
To find the value of a in a parabola opening up or down, subtract the y-value of the parabola at the vertex from the y-value of the point on the parabola that is one unit to the of the vertex?
right
To find the value of a in a parabola opening left or right subtract the x value of the parabola at the vertex from the x value of the point on the parabola that is one unit the vertex?
Above
What is the parabola equation?
the equation of a parabola is: y = a(x-h)^2 + k *h and k are the x and y intercepts of the vertex respectively * x and y are the coordinates of a known point the curve passes though * solve for a, then plug that a value back into the equation of the parabola with out the coordinates of the known point so the equation of the curve with the vertex at (0,3) passing through the point (9,0) would be.. 0 = a (9-0)^2 + 3 = 0 = a (81) + 3 = -3/81 = a so the equation for the curve would be y = -(3/81)x^2 + 3
The vertex of the parabola below is at the point 4 -1 which equation be this parabola's equation?
5
What are the coordinates of the vertex of the parabola described by the equation below?
The coordinates will be at the point of the turn the parabola which is its vertex.
The vertex of the parabola below is at the point -2 1 Which of the equations below could be this parabolas equation?
Go study
The vertex of the parabola below is at the point -3 -5 Which of the equations below could be the equation of this parabola?
2
The vertex of the parabola below is at the point (-4-2) which equation below could be one for parabola?
-2
What the the vertex of a parabola?
The vertex would be the point where both sides of the parabola meet.
A parabola that opens upward?
A parabola that opens upward is a U-shaped curve where the vertex is the lowest point on the graph. It can be represented by the general equation y = ax^2 + bx + c, where a is a positive number. The axis of symmetry is a vertical line passing through the vertex, and the parabola is symmetric with respect to this line. The focus of the parabola lies on the axis of symmetry and is equidistant from the vertex and the directrix, which is a horizontal line parallel to the x-axis.
The vertex of the parabola below is at the point 4 1 Which of the equations below could be this parabolas equation?
you didn't put any equations, but the answer probably begins with y= (x-4)^2+1
The is the extreme point of a parabola and is located halfway between the focus and directrix?
The vertex -- the closest point on the parabola to the directrix.
What is the lowest or highest point in a parabola?
A vertex is the highest or lowest point in a parabola.
Where is the point on the parabola for the maximum area?
The point on the parabola where the maximum area occurs is at the vertex of the parabola. This is because the vertex represents the maximum or minimum point of a parabolic function.
What is the point directly above the focus?
The point directly above the focus is the vertex of the parabola. The focus is a specific point on the axis of symmetry of the parabola, and the vertex is the point on the parabola that is closest to the focus.
