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.
To identify the dilation of a parabola, examine the coefficient of the quadratic term in its equation, typically in the form (y = ax^2 + bx + c). The value of (a) determines the dilation: if (|a| > 1), the parabola is narrower (stretched), while (|a| < 1) indicates it is wider (compressed). Additionally, a negative (a) reflects the parabola across the x-axis. Thus, the absolute value of (a) directly influences the shape and width of the parabola.
The value of ( b ) in a quadratic equation of the form ( y = ax^2 + bx + c ) affects the position and shape of the parabola. Specifically, it influences the location of the vertex along the x-axis and the direction in which the parabola opens. A larger absolute value of ( b ) can make the parabola wider or narrower depending on the value of ( a ), while the sign of ( b ) can shift the vertex left or right. Overall, these changes alter how the parabola intersects with the x-axis and its symmetry.
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A quadratic equation in vertex form is expressed as ( y = a(x - h)^2 + k ), where ((h, k)) is the vertex of the parabola. For a parabola with vertex at ((11, -6)), the equation becomes ( y = a(x - 11)^2 - 6 ). The value of (a) determines the direction and width of the parabola. Without additional information about the parabola's shape, (a) can be any non-zero constant.
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.
if the value is negative, it opens downard
To find the value of a in a parabola opening up or down subtract the y-value of the parabola at the vertex from the y-value of the point on the parabola that is one unit to the right of the vertex.
A parabola has a minimum value when it looks like the letter U
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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)
The vertex of this parabola is at -2 -3 When the y-value is -2 the x-value is -5. The coefficient of the squared term in the parabola's equation is -3.
The vertex of this parabola is at 5 5 When the x-value is 6 the y-value is -1. The coefficient of the squared expression in the parabola's equation is -6.
the first number out in front you pig
All of the points on a parabola define a parabola. However, the vertex is the point in which the y value is only used for one point on the parabola.
-5