University:
Santa Ana College
Course:
MATH 170 | Pre-Calculus Mathematics
Academic year:

2023
Views:

327

Pages:

2
Author:

TeveDiple38lh

Math 170 1) Given f (x ) = 5x 2 − 30x + 49 express the quadratic function in standard form. State the vertex and graph. Find the minimum value. 2) Given R (x ) = 23500x − 1000x 2 where R(x) is the revenue in dollars from selling tickets to a concert at price x. What ticket price results in the maximum revenue? What is the maximum revenue? 3) Sketch by hand: f (x ) = x 3 (x − 1)(x + 1)2 4) Divide x 3 + 2x 2 − 3x + 1 by x + 2 5) Find a fourth degree polynomial function with zeros of x = -3, 1, and 2 6) Given f (x ) = x 6 − 2x 5 − x 4 + 4x 3 − x 2 − 2x + 1 how many possible rational zeros can this function have? List them 7) Find the exact zeros of f (x ) = x 3 − 6x + 4 8) Find the exact zeros for f(x), and put into factored form, f (x ) = 2x 5 − 10x 3 + 12x − x 4 + 5x 2 − 6 9) Given a = 3 + 2i and b = 7 – 2i find each….a + b, a – b, ab, a/b 10) Given that x = i is a zero, find all zeros of f (x ) = x 4 − 8x 3 + 21x 2 − 8x + 20 11) Find all asymptotes of P (x ) = 12) Sketch f (x ) = x2 +1 2x 2 − 5x − 3 4x 3 − 8x 2 + x + 3 x3 + x2 include all key details, intercepts, asymptotes Answers: 1) Standard form: y = 5(x − 3)2 + 4 , vertex (3,4) , minimum value is 4 2) the ticket price of $11.75 yields the maximum revenue of $138,062.50 3) degree 6 thus end behavior is that both ends go up, passes through (0,0) and (1,0) bounces off the point (-1,0) 4) x 2 − 3 + 7 x +2 5) (3 possible answers) y = x 4 − x 3 − 7 x 2 + 13x − 6 or y = x 4 + 3x 3 − 7 x 2 − 15x + 18 or y = x 4 − 2x 3 − 7x 2 + 20x − 12 6) 2 possible zeros ; 1 and -1 7) x = 2 and x = −1 ± 3 8) Zeros are 1 2 , ± 2, ± 3 ,f (x ) = (2x − 1)(x 2 − 2)(x 2 − 3) 9) 10, -4 + 4i , 25 + 8i, 17/53 + 20/53 i 10) Zeros are ±i, 4 ± 2i note f (x ) factors to f (x ) = (x 2 + 1)(x 2 − 8x + 20) 11) Horizontal Asymptote: y = ½, Vertical asymptotes x = -1/2 and x = 3 12) H.A. y = 4, V.A. x = 0, x = -1, no y-intercept, x-intercepts at x = 1, x = 1.5, x = -0.5

Math 170 Homework 3 Answers

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