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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
What else can I help you with?
What is the equation for the parabola with the vertex -3.0 that passes through the point 318?
To find the equation of a parabola with vertex at ((-3, 0)) that passes through the point ((3, 18)), we can use the vertex form of a parabola, (y = a(x + 3)^2). To determine the value of (a), substitute the point ((3, 18)) into the equation: [ 18 = a(3 + 3)^2 \implies 18 = a(6)^2 \implies 18 = 36a \implies a = \frac{1}{2}. ] Thus, the equation of the parabola is (y = \frac{1}{2}(x + 3)^2).
What equation describes a parabola that opens left or right and whose vertex is at the point h v?
The equation of a parabola that opens left or right with its vertex at the point ((h, v)) is given by ((y - v)^2 = 4p(x - h)), where (p) is the distance from the vertex to the focus. If (p > 0), the parabola opens to the right, and if (p < 0), it opens to the left.
What could be the equation of a parabola with its vertex at (-36).?
The equation of a parabola with its vertex at the point (-36, k) can be expressed in the vertex form as ( y = a(x + 36)^2 + k ), where ( a ) determines the direction and width of the parabola. If the vertex is at (-36), the x-coordinate is fixed, but the y-coordinate ( k ) can vary depending on the specific position of the vertex. If you'd like a specific example, assuming ( k = 0 ) and ( a = 1 ), the equation would be ( y = (x + 36)^2 ).
Which equation describes a parabola that opens left or right and whose vertex is at the point (hv)?
The equation that describes a parabola opening left or right with its vertex at the point ((h, k)) is given by ((y - k)^2 = 4p(x - h)), where (p) determines the direction and width of the parabola. If (p > 0), the parabola opens to the right, while if (p < 0), it opens to the left. Here, ((h, k)) represents the vertex coordinates.
How do you find the a value in a parabola?
To find the "a" value in a parabola, which determines its width and direction (opening upwards or downwards), you can use the standard form of a quadratic equation: (y = ax^2 + bx + c). If you have a specific point on the parabola and the values of (b) and (c), you can substitute these into the equation along with the coordinates of the point to solve for (a). Alternatively, if the parabola is in vertex form, (y = a(x-h)^2 + k), you can derive (a) using the vertex and another point on the curve.
The vertex of the parabola below is at the point 4 -1 which equation be this parabola's equation?
5
The vertex of the parabola below is at the point (5 -3). Which of the equations below could be the one for this parabolaus anything?
To determine the equation of a parabola with a vertex at the point (5, -3), we can use the vertex form of a parabola's equation: (y = a(x - h)^2 + k), where (h, k) is the vertex. Substituting in the vertex coordinates, we have (y = a(x - 5)^2 - 3). The value of "a" will determine the direction and width of the parabola, but any equation in this form with varying "a" values could represent the parabola.
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.
What is the equation for the parabola with the vertex -3.0 that passes through the point 318?
To find the equation of a parabola with vertex at ((-3, 0)) that passes through the point ((3, 18)), we can use the vertex form of a parabola, (y = a(x + 3)^2). To determine the value of (a), substitute the point ((3, 18)) into the equation: [ 18 = a(3 + 3)^2 \implies 18 = a(6)^2 \implies 18 = 36a \implies a = \frac{1}{2}. ] Thus, the equation of the parabola is (y = \frac{1}{2}(x + 3)^2).
What equation describes a parabola that opens left or right and whose vertex is at the point h v?
The equation of a parabola that opens left or right with its vertex at the point ((h, v)) is given by ((y - v)^2 = 4p(x - h)), where (p) is the distance from the vertex to the focus. If (p > 0), the parabola opens to the right, and if (p < 0), it opens to the left.
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.
