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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.
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When a parabola opens upward the y coordinate of the vertex is a what?
Opening up, the vertex is a minimum.
Determine whether the parabola y equals -x2 plus 15x plus 8 opens up down left or right?
when you have y=+/-x2 +whatever, the parabola opens up y=-(x2 +whatever), the parabola opens down x=+/-y2 +whatever, the parabola opens right x=-(y2 +whatever), the parabola opens left so, your answer is up
The maximum or minimum of a parabola depending on whether the parabola opens up or down?
A parabola opening up has a minimum, while a parabola opening down has a maximum.
If a is greater than 0 the parabola opens?
Upwards.
What is y equals x2 plus 2x plus 1 on a graph?
Interpreting that function as y=x2+2x+1, the graph of this function would be a parabola that opens upward. It would be equivalent to y=(x+1)2. Its vertex would be at (-1,0) and this vertex would be the parabola's only zero.
How does the value of a variable affect the direction the parabola opens?
If the value of the variable is negative then the parabola opens downwards and when the value of variable is positive the parabola opens upward.
If the parabola opens upward the vertex is called?
maximum point :)
If the parabola opens upward the vertex is called the?
maximum point :)
What way does the parabola open if a is greater than 0?
If a is greater than zero then the parabola opens upward.
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)
Which way does a parabola open when the coefficient of its x2 term a is a negative?
A parabola opens downward when the coefficient of its ( x^2 ) term (denoted as ( a )) is negative. This means that the vertex of the parabola is the highest point on the graph. Conversely, if ( a ) is positive, the parabola opens upward.
When a parabola opens upward the y coordinate of the vertex is a what?
Opening up, the vertex is a minimum.
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.
Which way does a parabola open when the coefficient of its y term a is negative?
When the coefficient of the y term ( a ) in the equation of a parabola is negative, the parabola opens downward. This means that its vertex is the highest point on the graph. Conversely, if ( a ) were positive, the parabola would open upward.
Why is any parabola that opens upward or downward a function?
It is a function because for every point on the horizontal axis, the parabola identified one and only one point in the vertical direction.
When does a parabola open upward?
A parabola opens upward when its leading coefficient (the coefficient of the (x^2) term in the quadratic equation (y = ax^2 + bx + c)) is positive. This means that as you move away from the vertex of the parabola in both the left and right directions, the values of (y) increase. Consequently, the vertex serves as the minimum point of the parabola.
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).
