given the function find and simplify

Question

given the function P(x)=45+3x-2x² find and simplify 3P(a+6)-17. Discuss how each value shifts/scales the function

Answer 1

P(x) = 45 +3x -2x^2 is a downward opening parabola with y intercept =45

3P(a+6)-17 vertically stretches the parabola by a factor of 3, and shifts the parabola to the left by 6 and down by 17

3P(a+6) -17 = 3[45+3(a+6)-2(a+6)^2 -17]

= 3[28+3a+18 -2(a^2 +12a +36]

=3[46 + 3a - 2a^2 -24a -72]

= 3(-2a^2 -21a -26)

=-6a^2 -63a - 78