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How do you know if a parabola has a minimum or maximum value?
When you look at the parabola if it opens downwards then the parabola has a maximum value (because it is the highest point on the graph) if it opens upward then the parabola has a minimum value (because it's the lowest possible point on the graph)
What way does the parabola open if a is greater than 0?
If a is greater than zero then the parabola opens upward.
If the parabola opens downward the vertex is called the?
The maximum point.
What is a parabola that opens to the right called?
It is a square root mapping. This is not a function since it is a one-to-many mapping.
When will parabola open down?
In classic geometry, it opens down when the directrix is above the focus.In analytical (coordinate) geometry, if the equation of the parabola isy = ax^2 + bx + c, it opens down if a < 0.
How does the value of c affect the direction the parabola opens?
if the value is negative, it opens downard
How does the coefficient of a affect the way the parabola opens?
The coefficient of ( a ) in the quadratic equation ( y = ax^2 + bx + c ) determines the direction in which the parabola opens. If ( a > 0 ), the parabola opens upwards, creating a "U" shape, while if ( a < 0 ), it opens downwards, resembling an upside-down "U." Additionally, the absolute value of ( a ) affects the width of the parabola; larger values of ( |a| ) result in a narrower parabola, while smaller values lead to a wider shape.
What direction does the parabola open?
If the equation of the parabola isy = ax^2 + bx + c, then it opens above when a>0 and opens below when a<0. [If a = 0 then the equation describes a straight line, and not a parabola!].
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.
Is the vertex the highest or lowest value in the parabola?
The vertex of a parabola represents the highest or lowest point depending on the direction it opens. If the parabola opens upwards, the vertex is the lowest point (minimum value). Conversely, if it opens downwards, the vertex is the highest point (maximum value).
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.
What a parabola the extreme point (which is the highest lowest or farthest point left or right) is called the?
The extreme point of a parabola is called the vertex. In a parabola that opens upwards, the vertex represents the lowest point, while in a parabola that opens downwards, it represents the highest point. The vertex is a crucial feature for understanding the shape and direction of the parabola.
What is conactivity of parabola?
The concavity of a parabola refers to the direction it opens: upwards or downwards. A parabola opens upwards if its leading coefficient (the coefficient of the quadratic term) is positive, resulting in a "U" shape. Conversely, it opens downwards if the leading coefficient is negative, forming an "n" shape. The vertex of the parabola represents the point of minimum or maximum value, depending on its concavity.
How does the value a affect the width of the parabola?
In a quadratic equation of the form (y = ax^2 + bx + c), the value of (a) determines the width of the parabola. If (|a|) is greater than 1, the parabola is narrower, indicating that it opens more steeply. Conversely, if (|a|) is less than 1, the parabola is wider, meaning it opens more gently. The sign of (a) also affects the direction of the opening: positive values open upwards, while negative values open downwards.
Determine in which direction the parabola opens y equals x2-7x plus 18?
A parabola opens upwards if the quadratic coefficient - the number before the "x2" is positive; downward if it is negative. Note that x2 is the same as 1x2.
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.
In which direction will this parabola open y-8(x plus 5)2 plus 2?
The given equation of the parabola is in the vertex form (y - 8 = a(x + 5)^2 + 2). Here, (a) is the coefficient of the squared term. Since the coefficient of ((x + 5)^2) is positive (as it's implied to be 1), the parabola opens upwards. Therefore, the parabola opens in the direction of positive y-values.
