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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.
Is the vertex the highest point of the parabola?
The vertex of a parabola is the highest point if the parabola opens downward, making it a maximum point. Conversely, if the parabola opens upward, the vertex is the lowest point, known as a minimum. Thus, whether the vertex is the highest or lowest point depends on the direction in which the parabola opens.
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.
The parabola opens downward the vertex is called?
The maximum.
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.
Is the vertex the highest point of the parabola?
The vertex of a parabola is the highest point if the parabola opens downward, making it a maximum point. Conversely, if the parabola opens upward, the vertex is the lowest point, known as a minimum. Thus, whether the vertex is the highest or lowest point depends on the direction in which the parabola opens.
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.
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.
How do you know if a parabola opens up or down?
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 parabola opens downward the vertex is called?
The maximum.
If the parabola opens downward the vertex is called the?
The maximum point.
How do you tell if a quadratic function is minimum value or a maximum vale?
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 the parabola opens upward the vertex is called?
maximum point :)
If the parabola opens upward the vertex is called the?
maximum point :)
