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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.
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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 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 is an equation that describes a parabola that opens left or right and whose vertex is at the point (h v)?
An equation that describes a parabola opening left or right with its vertex at the point ((h, v)) can be expressed as ((y - v)^2 = 4p(x - h)), where (p) determines the direction and width of the parabola. If (p > 0), the parabola opens to the right, and if (p < 0), it opens to the left.
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).
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 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 is an equation that describes a parabola that opens left or right and whose vertex is at the point (h v)?
An equation that describes a parabola opening left or right with its vertex at the point ((h, v)) can be expressed as ((y - v)^2 = 4p(x - h)), where (p) determines the direction and width of the parabola. If (p > 0), the parabola opens to the right, and if (p < 0), it opens to the left.
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 standard form of the equation of a parabola that opens up or down?
The standard form of the equation of a parabola that opens up or down is given by ( y = a(x - h)^2 + k ), where ( (h, k) ) is the vertex of the parabola and ( 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 form emphasizes the vertex's position and the effect of the coefficient ( a ) on the parabola's shape.
What The equation y ax2 describes a parabola. If the value of a is positive which way does the parabola open?
If the value of ( a ) in the equation ( y = ax^2 ) 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 value of ( y ) increases. Conversely, if ( a ) were negative, the parabola would open downwards.
What is the equation of a parabola with a vertex at 0 0 and a focus at 0 6?
The standard equation for a Parabola with is vertex at the origin (0,0) is, x2 = 4cy if the parabola opens vertically upwards/downwards, or y2 = 4cx when the parabola opens sideways. As the focus is at (0,6) then the focus is vertically above the vertex and we have an upward opening parabola. Note that c is the distance from the vertex to the focus and in this case has a value of 6 (a positive number). The equation is thus, x2 = 4*6y = 24y
How does finding the vertex of a parabola help you when graphing a quadratic equation?
Finding the vertex of the parabola is important because it tells you where the bottom (or the top, for a parabola that 'opens' downward), and thus where you can begin graphing.
How does an equation for a sideways parabola look like?
An equation for a sideways parabola can be expressed in the form ( y^2 = 4px ) for a parabola that opens to the right, or ( y^2 = -4px ) for one that opens to the left. Here, ( p ) represents the distance from the vertex to the focus. The vertex of the parabola is at the origin (0,0), and the axis of symmetry is horizontal. If the vertex is not at the origin, the equation can be adjusted to ( (y-k)^2 = 4p(x-h) ), where ((h, k)) is the vertex.
How do you write an equation of a parabola with vertex at the origin and the given focus 60?
To write the equation of a parabola with its vertex at the origin (0, 0) and a focus at (0, 60), you first identify the orientation of the parabola. Since the focus is above the vertex, the parabola opens upwards. The standard form of the equation for a parabola that opens upwards is ( y = \frac{1}{4p}x^2 ), where ( p ) is the distance from the vertex to the focus. Here, ( p = 60 ), so the equation becomes ( y = \frac{1}{240}x^2 ).
What equation describes a parabola that opens up or down and whose vertex at the point (hv)?
This is called the 'standard form' for the equation of a parabola:y =a (x-h)2+vDepending on whether the constant a is positive or negative, the parabola will open up or down.
