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You are watching: Parent function of a quadratic equation

The Parabola as a Parent duty betterworld2016.org Topical outline | Algebra 1 rundown | MathBits" Teacher sources Terms that Use contact Person: Donna Roberts
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For the family members of quadratic functions, y = ax2 + bx + c, the simplest functionof this kind is y = x2.
The "Parent" Graph:
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The simplest parabola is y = x2, whose graph is shown at the right. The graph passes with the origin (0,0), and also is included in Quadrants I and also II.

This graph is well-known as the "Parent Function" for parabolas, or quadratic functions. All various other parabolas, or quadratic functions, can be acquired from this graph through one or an ext 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 your memories that transformations and let"s take a quick look in ~ what is possible.

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


move the graph vertically - increase or down y = x2+ k y = x2+ 4 move the graph increase 4 units y = x2- 4 moves 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 systems y = (x + 2)2moves the graph LEFT 2 systems
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flip the graph end 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 that the coordinates) y = (-x)2 y = x2 parental graph y = (-x)2 parental reflected over y-axis
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stretches far from the x-axis or compresses towards 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 vertical stretch
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stretches far from the y-axis or compresses towards the y-axis y = (a • x)2 | a | > 1 is a compression by element of 1/a; 0 y = x2 parental graph y = (¼x)2 horizontal big y = (4x)2 horizontal compression
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Topical outline | Algebra 1 overview | betterworld2016.org | MathBits" Teacher sources Terms the Use call Person: Donna Roberts