Combination of Horizontal and Vertical Shift In this quadratic function K determines the amount of steps and the vertical direction in which the function will shift - upwards or downwards. P determines the amount of steps and the horizontal direction in which the function will shift - to the right or to the left.
Let's look at an example of combining both displacements together.
For example, in the function: y=(x−4)2+3
The changes will be: according to P=4 -The parabola will shift 4 steps to the right. According to K=3 -The parabola will shift 3 steps upwards.
Let's see it in the illustration:
We can see that the vertex of the parabola is: (4,3)
Zero Point or Root of the Function - Graphical and Algebraic Solution whenY=0
The zeros of a function are the intersections with the X axis.
Algebraic Solution
when K positive - This equation has no solution except in the case where K equals0 and also P equalsX. when K negative- Generally, this equation will have 2 solutions.
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Question 1
Find the corresponding algebraic representation of the drawing: