(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
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 ).
The vertex of a parabola that opens down is called the maximum point. This point represents the highest value of the function described by the parabola, as the graph decreases on either side of the vertex. In a quadratic equation of the form (y = ax^2 + bx + c) where (a < 0), the vertex can be found using the formula (x = -\frac{b}{2a}). The corresponding (y)-value can then be calculated to determine the vertex's coordinates.
A vertex is the highest or lowest point in a parabola.
right
Above
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The coordinates will be at the point of the turn the parabola which is its vertex.
Go study
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The vertex would be the point where both sides of the parabola meet.
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.
you didn't put any equations, but the answer probably begins with y= (x-4)^2+1
The vertex -- the closest point on the parabola to the directrix.
A vertex is the highest or lowest point in a parabola.
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.
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.