y=x^2 +4x-12, Find the Range (co-domain) when the domain of x is (1) -6 to 2 inclusive (2) the set of real numbers, R.

This question usually comes up at AS level where students have prior knowledge of quadratic functions:We need to 1) understand the 'shape' 2) locate the roots 3) Find the turning point 4) sketch the graph 5) answer1) Quadratic graphs have the x^2 functional form. This produces a 'smiley face'. (Draw)2) Some quadratic graphs intersect the x-axis, some don't. (Draw) The points where the smiley face intersects the axis are the roots. We can have 2, 1, or none.3) The turning point is the lowest tip of the smiley face.4) The 'domain' is all the values x can take, the 'range' is all the values y can takeTurning to our example:1&2) Roots: x = -6, 2 3)Turning point: (-2, -16) 4)(now sketch)5) when x in [-6,2] y in [-16,0] when x in R, y in [-16,inf)

PT
Answered by Pascal T. Maths tutor

2704 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Time, T, is measured in tenths of a second with respect to distance x, is given by T(x)= 5(36+(x^2))^(1/2)+4(20-x). Find the value of x which minimises the time taken, hence calculate the minimum time.


Find a solution for the differential equation dy/dx=exp(-y)*sin2x which passes through the origin.


When do we use the quadratic formula, and when the completing the square method?


How can I improve my score?


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