Let f(x) = a(x −p )^2 + q be a quadratic function, where a, p,q are constants and a ≠ 0. f(x) is translated up by k units, translated right by c units, and then take a reciprocal of the translated function. Define f(x) be the function after performing all the transformations. a. Find the conditions on the constants a, q and k so that g(x) does not have a vertical asymptote.

b. Find the x value(s) so that there is/are invariant point(s) linking f(x) and 1/f(x).

Solve the following simultaneous equation by using an algebraic method (either substitution or elimination) 2x + 3y=-4 4x-y=11

Guys i need ! graded assignment grade 8 checkpoint 2, part 2 answer the questions below. when you are finished, submit this assignment to your teacher by the due date for full credit. total score: of 9 points (score for question 1: of 4 points) 1. the cost of renting a car for a day is $0.50 per mile plus a $15 flat fee. (a) write an equation to represent this relationship. let x be the number of miles driven and y be the total cost for the day. (b) what does the graph of this equation form on a coordinate plane? explain. (c) what is the slope and the y-intercept of the graph of the relationship? explain.

At the "no mutants allowed" country farm, every sheep has 4 legs, every chicken has two legs, and all animals have only 1 head. asked to count how many sheep and chicken are in the fields, a farm boy reports back that there are 140 feet and 50 heads. how many sheep and chicken are there? there are sheep and chicken at the farm.