15 (a) Write $x^2 - 8x + 25$ in the form $(x - a)^2 + b$ - OCR - GCSE Maths - Question 15 - 2018 - Paper 1
Question 15
15 (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 $y = x^2 - 8x + 25$. (c) Hence descri... show full transcript
Worked Solution & Example Answer:15 (a) Write $x^2 - 8x + 25$ in the form $(x - a)^2 + b$ - OCR - GCSE Maths - Question 15 - 2018 - Paper 1
Step 1
Write $x^2 - 8x + 25$ in the form $(x - a)^2 + b$
96%
114 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
To rewrite the quadratic expression, we will complete the square.
Start with the expression:
x2−8x+25
Take half of the coefficient of x (which is −8), square it, and add/subtract this inside the expression:
x2−8x+16−16+25
This simplifies to:
(x−4)2+9
Thus, we rewrite:
x2−8x+25=(x−4)2+9
Step 2
Write down the coordinates of the turning point of the graph of $y = x^2 - 8x + 25$
99%
104 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
The turning point of the graph can be found from the completed square form:
From the expression (x−4)2+9, the vertex form reveals that the turning point is at:
x-coordinate: 4
y-coordinate: 9
Thus, the coordinates are (4, 9).
Step 3
Hence describe the single transformation which maps the graph of $y = x^2$ onto the graph of $y = x^2 - 8x + 25$
96%
101 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
The transformation can be described as a translation:
Translate the graph of y=x2 4 units to the right and 9 units upwards.
