A positive quadratic coefficient causes the ends of the parabola to point upward. A negative quadratic coefficient causes the ends of the parabola to point downward. The greater the quadratic coefficient, the narrower the parabola. The lesser the quadratic coefficient, the wider the parabola .
a determines the width and the direction of the parabola : The larger |a| becomes, the wider the parabola. If a is positive, the parabola opens upward, and if a is negative, the parabola opens downward.
Also, how do you know if a parabola is narrow or wide? A large positive value of a makes a narrow parabola ; a positive value of a which is close to 0 makes the parabola wide. If a<0 in f(x)=ax2+bx+c, the parabola opens downward. In this case the vertex is the maximum, or highest point, of the parabola.
The width is the length of the secant line segment through the parabola's focus parallel to the directrix, also known as the latus rectum.
If the x is squared, the parabola is vertical (opens up or down). If the y is squared, it is horizontal (opens left or right). If a is positive, the parabola opens up or to the right. If it is negative, it opens down or to the left.
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As we can see from the graphs, when 0 < |a| < 1 (|a| means absolute value of a), the parabola appears wider. When |a| > 1, the parabola appears thinner. When a is positive, the parabola opens upwards; when a is negative, the parabola opens downward.
A parabola can have 2 x-intercepts, 1 x-intercept or zero real x intercepts. If the parabola only has 1 x-intercept (see middle of picture below), then the parabola is said to be tangent to the x-axis.
It works this way:If a is positive (a > 0), then the reference parabola is not reflected over the x-axis. if a is negative (a < 0), then the reference parabola is reflected across the x-axis. The reference parabola is stretched or compressed by the size, or absolute value, of a.
The graph of a quadratic function is a U-shaped curve called a parabola. It can be drawn by plotting solutions to the equation, by finding the vertex and using the axis of symmetry to plot selected points, or by finding the roots and vertex. The standard form of a quadratic equation is .
To find the width:Calculate the range of the entire data set by subtracting the lowest point from the highest, Divide it by the number of classes. Round this number up (usually, to the nearest whole number).
The function f(x)=x2 is not one-to-one because f(2) = f(-2). Its graph is a parabola, and many horizontal lines cut the parabola twice. The function f(x)=x 3, on the other hand, IS one-to-one. If two real numbers have the same cube, they are equal.
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