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You are watching: For which graph is the parent function ?

The Parabola as a Parent role ubraintv-jp.com Topical rundown | Algebra 2 overview | MathBits" Teacher sources Terms the Use contact Person: Donna Roberts
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For the family of quadratic functions, y = ax2 + bx + c, the simplest functionof this type is y = x2.
The "Parent" Graph:
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The simplest parabola is y = x2, whose graph is displayed at the right. The graph passes v the origin (0,0), and also is had in Quadrants I and also II.

This graph is known as the "Parent Function" because that parabolas, or quadratic functions. All other parabolas, or quadratic functions, deserve to be acquired from this graph through one or much more transformations.

The "Children" Graphs:
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The "parent" parabola can offer birth to a myriad of other parabolic forms through the process of transformations.

Brush off her memories of transformations and let"s take a rapid look in ~ what is possible.

When graphing quadratic features (parabolas), keep in mind the two creates of equations may be used: y = ax2 + bx + c or y = a(x - h)2 + k


move the graph vertically - up or down y = x2+ k y = x2+ 4 moves the graph up 4 systems y = x2- 4 move the graph under 4 devices

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move the graph horizontally - left or right y = (x - h)2 y = (x - 4)2 moves the graph best 4 units y = (x + 2)2 moves the graph LEFT 2 devices
flip the graph over the x-axis (negates the y-values of the coordinates)y = -(x2) y = x2 parental graph y = -(x2) parent reflected over x-axis
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flip the graph over the y-axis (negates the x-values the the coordinates) y = (-x)2 y = x2 parental graph y = (-x)2 parent reflected end y-axis
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stretches far from the x-axis or compresses toward the x-axis y = a • x2 | a | > 1 is a stretch; 0 y = x2 parent graph y = ¼(x)2 upright compression y = 4(x)2 upright stretch
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stretches away from the y-axis or compresses toward the y-axis y = (a • x)2 | a | > 1 is a compression by variable of 1/a; 0 y = x2 parent graph y = (¼x)2 horizontal large y = (4x)2 horizontal compression
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Topical overview | Algebra 2 synopsis | ubraintv-jp.com | MathBits" Teacher resources Terms the Use contact Person: Donna Roberts