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You are watching: The parent function of a quadratic equation

The Parabola together a Parent function benidormclubdeportivo.org Topical overview | Algebra 1 summary | MathBits" Teacher resources Terms of Use call Person: Donna Roberts
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For the family of quadratic functions, y = ax2 + bx + c, the easiest functionof this kind is y = x2.
The "Parent" Graph:
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The most basic parabola is y = x2, who graph is displayed at the right. The graph passes with the origin (0,0), and is consisted of in Quadrants I and II.

This graph is recognized as the "Parent Function" for parabolas, or quadratic functions. All various other parabolas, or quadratic functions, have the right to be obtained from this graph by one or an ext transformations.


The "Children" Graphs:
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The "parent" parabola can give birth come a myriad of other parabolic shapes through the process of transformations.

Brush off your memories of transformations and also let"s take a quick look in ~ what is possible.

When graphing quadratic attributes (parabolas), store in mind that two creates of equations might 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 increase 4 devices y = x2- 4 moves the graph down 4 units

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move the graph horizontally - left or right y = (x - h)2 y = (x - 4)2 moves the graph ideal 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 that the coordinates)y = -(x2) y = x2 parental graph y = -(x2) parental reflected over x-axis
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flip the graph end 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 away from the x-axis or compresses toward the x-axis y = a • x2 | a | > 1 is a stretch; 0 y = x2 parental graph y = ¼(x)2 vertical compression y = 4(x)2 upright stretch
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stretches away 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 = x)2 horizontal large y = (4x)2 horizontal compression
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Topical summary | Algebra 1 outline | benidormclubdeportivo.org | MathBits" Teacher resources Terms the Use contact Person: Donna Roberts