Let f(x) = x^2 - 1. A vertical translation of 3 and a horizontal translation of -2 is applied. Write the new function g(x) in the form g(x) = ax^2 + bx + c

Let f(x) = x2- 1To apply a vertical translation, simply add the value to the overall equation. In this case it is positive and thus moves the graph up 3 units:f(x) = x2- 1 + 3 = x2+ 2To apply a horizontal translation, recall the form g(x) = (x-a)2+b; a denotes the horizontal translation, and in this case:g(x) = (x+2)2+ 2 [this translates the graph 2 units to the left]Finally, convert to the form ax2+ bx + c. This can be done by expanding the equation above:g(x) = (x+2)2+ 2= (x+2)(x+2) + 2= x2+ 4x + 4 + 2= x2+ 4x + 6 [ANSWER]

JH
Answered by Jack H. Maths tutor

2556 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

Sketch the graph of y = 5 - 7x


What is 90 million in standard form?


John bought 7 bags of cement and 3 bags of gravel with the total weight of 215kgs. Shona bought 5 bags of cement and 4 bags of gravel with the total weight of 200kgs. How much does 1 bag of cement weigh and how much does 1 bag of gravel weigh?


Work out: 0.7 + 3/5


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning