066sketch(x.h)2

 Year 9 into 10 Step Up Program  11E


 * Parabolas **toc

Sketching y = (x – h)²
The question today is:

What happens if we add (or subtract) a number from the x inside the part being squared?

** Question 1 **
Fill out a table of values for y = (x – 2)² Then sketch the graph. Label the graph with coordinates of the turning point and the y-intercept.
 * h = 2

What is different between this graph and the standard y = x²?

Based on this example, what do you think the rule is for y = (x – 2)² ?

** Solution 1 **
Table of values for y = (x – 2)² :

Graph shown to the right:

Notice that the graph has __shifted to the right__ by 2 units.

This is the __opposite__ direction to the sign of the value in the brackets.

The turning point was __translated 2 to the right__.

The turning point has coordinates (2, 0)

The axis of symmetry is : x = 2

The y-intercept is at (0, 4) {where x = 0}

Rule for y = (x – h)²

 * The value with the x shifts the parabola to the left or the right.
 * The shift is in the opposite direction to the sign
 * The turning point will be at (h, 0)
 * The axis of symmetry will be at x = h
 * the y-intercept can be found by subsituting x = 0 into the rule

Note: The turning point occurs where the insides of the bracket are equal to 0.



** Example **
To sketch y = (x + 3)²
 * the parabola is shifted to the __left__ by 3
 * the turning point is at (–3, 0)
 * the axis of symmetry is x = –3
 * the y-intercept occurs where x = 0
 * y-intercept (0, 9)

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