 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that find an equation for the reflection of the function f of x is equal to 5 x square plus 2 x minus 3 across x axis and y axis. We know that y is equal to minus of f of x is an equation for reflection of function y is equal to f of x across x axis and y is equal to f of minus x is an equation for reflection of function y is equal to f of x across y axis. With this key idea let us proceed to the solution. According to the question we need to find an equation for the reflection of this function f of x across x axis and y axis. Now using this key idea we will find the equation for the reflection of the function f of x is equal to 5 x square plus 2 x minus 3 across x axis and y axis. First we find equation for reflection across x axis and it is given by y is equal to minus of f of x so we multiply this given function with negative sign we get y is equal to minus of 5 x square plus 2 x minus 3 the whole which implies that y is equal to minus of 5 x square minus of 2 x plus 3 so y is equal to minus of 5 x square minus of 2 x plus 3 is the required equation for reflection in x axis. Now we find equation for reflection in y axis using this key idea we know that y is equal to f of minus x is an equation for reflection of the function y is equal to f of x across y axis from the key idea we have the equation for reflection in y axis is given by y is equal to f of minus x so we replace x by minus x in the given function and we get y is equal to 5 minus x whole square plus 2 into minus x minus 3 which implies that y is equal to 5 minus x whole square is x square plus 2 into minus x is minus 2 x minus 3 that is y is equal to 5 x square minus 2 x minus 3 so y is equal to 5 x square minus 2 x minus 3 is the required equation for reflection in y axis which is the required answer this completes our session hope you enjoyed this session