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How do you graph y equals x2?
The graph is a parabola facing (opening) upwards with the vertex at the origin.
Given the standard equation for a parabola opening up or down which way does a parabola open when the coefficient of the x2 term a is positiveUp or down?
In that case it opens upwards.
How can you tell if a porabola is opening up or down using ax2 plus bx plus c?
If a is positive, then the parabola opens upwards; if negative, then it opens downwards.
If a is greater than 0 the parabola opens?
Upwards.
Can a parabola have both a maximum and minimum point?
No, a parabola cannot have both a maximum and minimum point. A parabola opens either upwards or downwards; if it opens upwards, it has a minimum point, and if it opens downwards, it has a maximum point. Thus, a parabola can only have one of these extrema, not both.
If a is positive which way does the parabola open?
Upwards like a letter U
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
When the parabola concave downward and upward?
If the number in front of the x squared is negative, then the parabola will open upwards. The opposite occurs when the number is positive.
How do you graph yx2?
To graph the equation ( y = x^2 ), first recognize that it represents a parabola opening upwards. Plot key points, such as ( (0, 0) ), ( (1, 1) ), ( (-1, 1) ), ( (2, 4) ), and ( (-2, 4) ). Connect these points smoothly, ensuring the curve is symmetric about the y-axis. The vertex of the parabola is at the origin, and the graph will extend infinitely upwards as ( x ) moves away from zero.
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.
How do you find the a value in a parabola?
To find the "a" value in a parabola, which determines its width and direction (opening upwards or downwards), you can use the standard form of a quadratic equation: (y = ax^2 + bx + c). If you have a specific point on the parabola and the values of (b) and (c), you can substitute these into the equation along with the coordinates of the point to solve for (a). Alternatively, if the parabola is in vertex form, (y = a(x-h)^2 + k), you can derive (a) using the vertex and another point on the curve.
What is the extreme point of a parabola?
The extreme point it the highest or lowest point of the parabola (depending if it is concave downwards or upwards). It is the point of the parabola tat is closest to the focus. the extreme point lies on the axis of symmetry.
