A)Write x^2 – 8x + 25 in the form (x – a)^ 2 + b. (B) Write down the coordinates of the turning point of the graph of y = x2 – 8x + 25. (C)Hence describe the single transformation which maps the graph of y = x2 onto the graph of y = x2 – 8x + 25.
This is a question about completing the square of a quadratic equation. This is used to find the minimum point on a parabolic graph. A) Step 1 - set up the '(x – a)2' term by dividing the coefficient of x by 2:=(x-4)2 Step 2 - take away the square of the 'a' term:=(x-4)2 -(-4)2+25Step 3 - Simplify. Remember that a negative number squared is positive (negative X negative = positive). But also remember the negative sign in front of the 4.=(x-4)2 -16+25=(x-4)2 +9B) The answer to this type of question is always (-a,b). Again remember that a negative X a negative = positive. Therefore the answer is (4,9)C) You know that the graph y=x2 has a minimum point of (0,0), so we have to work out how to get from (0,0) to (4,9). This is simply a translation with a vector (4,9). Remember the key words 'translation', 'rotation', and 'enlargement'. These are all different forms of transformations.
