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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?
The equation below describes a parabola. If a is positive which way does the parabola open?
If the coefficient ( a ) in the equation of a parabola (typically given in the form ( y = ax^2 + bx + c )) is positive, the parabola opens upwards. This means that the vertex of the parabola is the lowest point, and as you move away from the vertex in either direction along the x-axis, the y-values increase.
Which equation describes a parabola that opens up or down and whose vertex is at the point (h v)?
The equation that describes a parabola that opens up or down with its vertex at the point (h, v) is given by the vertex form of a quadratic equation: ( y = a(x - h)^2 + v ), where ( a ) determines the direction and width of the parabola. If ( a > 0 ), the parabola opens upwards, while if ( a < 0 ), it opens downwards.
Which equation describes a parabola that opens up or down and whose vertex is at the point (hv)?
The equation that describes a parabola opening up or down with its vertex at the point ((h, v)) is given by (y = a(x - h)^2 + v), where (a) is a non-zero constant. If (a > 0), the parabola opens upwards, while if (a < 0), it opens downwards. The vertex form allows easy identification of the vertex and the direction of the parabola's opening.
What equation describes a parabola that opens up or down and whose vertex is at the point (h v)?
The equation that describes a parabola opening up or down with its vertex at the point ((h, v)) is given by the standard form (y = a(x - h)^2 + v), where (a) determines the direction and width of the parabola. If (a > 0), the parabola opens upward, while if (a < 0), it opens downward. The vertex ((h, v)) is the minimum or maximum point of the parabola, depending on the sign of (a).
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).
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
The equation below describes a parabola. If a is positive which way does the parabola open?
If the coefficient ( a ) in the equation of a parabola (typically given in the form ( y = ax^2 + bx + c )) is positive, the parabola opens upwards. This means that the vertex of the parabola is the lowest point, and as you move away from the vertex in either direction along the x-axis, the y-values increase.
Which equation describes a parabola that opens up or down and whose vertex is at the point (h v)?
The equation that describes a parabola that opens up or down with its vertex at the point (h, v) is given by the vertex form of a quadratic equation: ( y = a(x - h)^2 + v ), where ( a ) determines the direction and width of the parabola. If ( a > 0 ), the parabola opens upwards, while if ( a < 0 ), it opens downwards.
Which equation describes a parabola that opens up or down and whose vertex is at the point (hv)?
The equation that describes a parabola opening up or down with its vertex at the point ((h, v)) is given by (y = a(x - h)^2 + v), where (a) is a non-zero constant. If (a > 0), the parabola opens upwards, while if (a < 0), it opens downwards. The vertex form allows easy identification of the vertex and the direction of the parabola's opening.
What equation describes a parabola that opens up or down and whose vertex is at the point (h v)?
The equation that describes a parabola opening up or down with its vertex at the point ((h, v)) is given by the standard form (y = a(x - h)^2 + v), where (a) determines the direction and width of the parabola. If (a > 0), the parabola opens upward, while if (a < 0), it opens downward. The vertex ((h, v)) is the minimum or maximum point of the parabola, depending on the sign of (a).
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 the the vertex of a parabola?
The vertex would be the point where both sides of the parabola meet.
