It is a function because for every point on the horizontal axis, the parabola identified one and only one point in the vertical direction.
The maximum.
maximum point :)
Opens downward.
Yes, a parabola can represent the graph of a function, specifically a quadratic function of the form ( y = ax^2 + bx + c ). However, not all parabolic shapes qualify as a function; for instance, if a parabola opens sideways (like ( x = ay^2 + by + c )), it fails the vertical line test, which states that a function must have only one output for each input. Thus, while upward or downward-opening parabolas are indeed functions, sideways-opening parabolas are not.
In a quadratic equation of the form ( ax^2 + bx + c = 0 ), the coefficient ( a ) represents the leading coefficient that determines the shape and orientation of the parabola. If ( a > 0 ), the parabola opens upward, while if ( a < 0 ), it opens downward. Additionally, the value of ( a ) affects the width of the parabola; larger absolute values of ( a ) result in a narrower parabola, while smaller absolute values lead to a wider shape.
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.
The maximum.
I think it's like this: x2+3x-5 So if the x2 part is a positive then it opens upward but if it's negative it goes downward.
The maximum point.
maximum point :)
maximum point :)
Standard notation for a quadratic function: y= ax2 + bx + c which forms a parabola, a is positive , minimum value (parabola opens upwards on an x-y graph) a is negative, maximum value (parabola opens downward) See related link.
If a is greater than zero then the parabola opens upward.
Opens downward.
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)
Opening up, the vertex is a minimum.
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.