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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.
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.
What is the shape of the graph of a quadratic function?
The graph of a quadratic function is a parabola. It can open either upward or downward depending on the sign of the coefficient of the squared term; if it is positive, the parabola opens upward, and if negative, it opens downward. The vertex of the parabola is its highest or lowest point, and the axis of symmetry is a vertical line that runs through this vertex.
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.
If a is positive which way does a parabola open?
If ( a ) is positive in the quadratic equation ( y = ax^2 + bx + c ), the parabola opens upward. This means that the vertex of the parabola is the lowest point on the graph, and as you move away from the vertex in either direction along the x-axis, the values of ( y ) increase. Conversely, if ( a ) were negative, the parabola would open downward.
if the parabola open upward a is?
positive.
What way does the parabola open if a is greater than 0?
If a is greater than zero then the parabola opens upward.
Which way does a parabola open when the coefficent of its x2-term a is negative?
Opens downward.
In which directions does this hyperbola open?
X2 + whatever would open upward. - X2 + whatever would open downward. y2 + whatever would open to the right. - y2 + whatever would open to the left.
What does changing the value of a from a negative number to a positive number cause the parabola to do?
open upward
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 does changing the value form a positive number to a negative number cause a parabola to do?
Changing the value of a parabola's coefficient from positive to negative causes the parabola to open downward instead of upward. This transformation affects the vertex's position and the overall direction of the graph. As a result, the maximum point becomes the vertex, while the minimum point is no longer defined. The shape is inverted, leading to different intercepts and behavior in relation to the x-axis.
