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You are watching: Which of the following is the quadratic parent function

The Parabola together a Parent duty chrischona2015.org Topical overview | Algebra 1 overview | MathBits" Teacher resources Terms the Use call Person: Donna Roberts
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For the family of quadratic functions, y = ax2 + bx + c, the most basic functionof this kind is y = x2.
The "Parent" Graph:
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The most basic parabola is y = x2, whose graph is presented at the right. The graph passes with the beginning (0,0), and is contained in Quadrants I and II.

This graph is known as the "Parent Function" for parabolas, or quadratic functions. All other parabolas, or quadratic functions, can be acquired from this graph by one or much more transformations.


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

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

When graphing quadratic features (parabolas), store in mind that 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 move the graph increase 4 devices y = x2- 4 moves the graph down 4 devices

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move the graph horizontally - left or right y = (x - h)2 y = (x - 4)2 move the graph best 4 units y = (x + 2)2moves the graph LEFT 2 systems
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flip the graph over the x-axis (negates the y-values of the coordinates)y = -(x2) y = x2 parental graph y = -(x2) parent reflected end 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 parent graph y = (-x)2 parental reflected end 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 upright compression y = 4(x)2 upright stretch
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stretches far from the y-axis or compresses toward the y-axis y = (a • x)2 | a | > 1 is a compression by element of 1/a; 0 y = x2 parent graph y = x)2 horizontal stretch y = (4x)2 horizontal compression
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Topical overview | Algebra 1 synopsis | chrischona2015.org | MathBits" Teacher resources Terms the Use contact Person: Donna Roberts