Question

a teacher asked her students to think of a number, multiply by 5, and subtract the product from 20 , then she asked them to multiply the resulting difference by the number they first thougt of

a) use function notation to express the final answer in terms of the orginal number

b)determine the outputs for the input numbers 1, -1, & 7

c) determine the maximum result possible

I need help with this question i am so confused!!!!

Answer 1

think of a number -- x
multiply by 5 ---> 5x
subtract that product from 20 ---> 20 - 5x
multiply that by original number --> x(20-5x)
= -5x^2 + 20x

b) just put in each of the given values
e.g. for x=7
result = -5(49) + 20(7) = -105

c) let y = -5x^2 + 20x
this is represented by a parabola which opens downwards, so the y value of the vertex is the maximim

Since you are dealing with this type of question, I assume that you have been taught how to find the vertex of a parabola.