You are watching: The parent function of a quadratic equation
For the family of quadratic functions, y = ax2 + bx + c, the easiest functionof this kind is y = x2.
The "Children" Graphs:
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
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
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
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
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
See more: How Many Calories Are In A Fried Chicken Wing S, Calories In Flour
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 = (¼x)2 horizontal large y = (4x)2 horizontal compression
Topical summary | Algebra 1 outline | benidormclubdeportivo.org | MathBits" Teacher resources Terms the Use contact Person: Donna Roberts