Explanation Given: The x -coordinates of the vertex of f ( x ) = a x 2 + b x + c , a ≠ 0 . Calculation: Let us consider the general quadratic equation of the form f ( x ) = a x 2 + b x + c , where a , b and c are real numbers and a ≠ 0 . Simplified the function f ( x ) = a x 2 + b x + c and make it into perfect square form as, f ( x ) = a ( x 2 + b a x + c a ) = a ( x 2 + 2 b 2 a x + b 2 4 a 2 − b 2 4 a 2 + c a ) = a ( x + b 2 a ) 2 + ( 4 a c − b 2 4 a 2 ) = a ( x − h ) 2 + k Where h = − b 2 a and k = 4 a c − b 2 4 a 2 ...

10th Edition

ISBN: 9780321979476

Author: Michael Sullivan

Publisher: PEARSON

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Question

Chapter 4.3, Problem 7CV

To determine

To fill: The $x -coordinates$ of the vertex of $f (x) = a x^{2} + b x + c$ , $a \neq 0$ , is __________.

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Chapter 4.3, Problem 6CV

Chapter 4.3, Problem 8CV

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1. (20 pts) Determine whether the following statements are true (T) or false (F)? (A reasoning is required.) (1) Let V be the set of all ordered pairs of real numbers. Consider the following addition and scalar multiplication operations on u = u= (u1, u2) and v = (v1, v2): u + v = (U₁ + V₁, U₂ + v₂), ku = (ku₁, u₂). Is V a vector space under the above operations? U2 (2) The set Mmxn of all m×n matrices with the usual operations of addition and scalar multiplication is a vector space. α (3) The dimension of the vector space of all matrices A = [a b] in R2×2 with a+d=0 is 4. (4) The coordinate vector of p(x) = 2-x+x² in P3 relative to the basis S = {1, 1+x, x + x2} is [4 -2 1]. (5) If a 6×4 matrix A has a rank 3, then the dimension of N(A) is 3.

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For the spinner below, assume that the pointer can never lie on a borderline. Find the following probabilities. (enter the probabilities as fractions)

Chapter 4 Solutions

College Algebra (10th Edition)

Ch. 4.1 - Prob. 1AYP Ch. 4.1 - Prob. 2AYP Ch. 4.1 - Prob. 3AYP Ch. 4.1 - Prob. 4AYP Ch. 4.1 - Prob. 5AYP Ch. 4.1 - Prob. 6AYP Ch. 4.1 - Prob. 7CV Ch. 4.1 - Prob. 8CV Ch. 4.1 - Prob. 9CV Ch. 4.1 - Prob. 10CV

Ch. 4.1 - Prob. 11CV Ch. 4.1 - Prob. 12CV Ch. 4.1 - Prob. 13SB Ch. 4.1 - Prob. 14SB Ch. 4.1 - Prob. 15SB Ch. 4.1 - Prob. 16SB Ch. 4.1 - Prob. 17SB Ch. 4.1 - Prob. 18SB Ch. 4.1 - Prob. 19SB Ch. 4.1 - Prob. 20SB Ch. 4.1 - Prob. 21SB Ch. 4.1 - Prob. 22SB Ch. 4.1 - Prob. 23SB Ch. 4.1 - Prob. 24SB Ch. 4.1 - Prob. 25SB Ch. 4.1 - Prob. 26SB Ch. 4.1 - Prob. 27SB Ch. 4.1 - Prob. 28SB Ch. 4.1 - Prob. 29AE Ch. 4.1 - Prob. 30AE Ch. 4.1 - Prob. 31AE Ch. 4.1 - Prob. 32AE Ch. 4.1 - Prob. 33AE Ch. 4.1 - Prob. 34AE Ch. 4.1 - Prob. 35AE Ch. 4.1 - Prob. 36AE Ch. 4.1 - Prob. 37AE Ch. 4.1 - Prob. 38AE Ch. 4.1 - Prob. 39AE Ch. 4.1 - Prob. 40AE Ch. 4.1 - Prob. 41AE Ch. 4.1 - Prob. 42AE Ch. 4.1 - Prob. 43AE Ch. 4.1 - Prob. 44AE Ch. 4.1 - Prob. 45AE Ch. 4.1 - Prob. 46AE Ch. 4.1 - Prob. 47AE Ch. 4.1 - Prob. 48AE Ch. 4.1 - Prob. 49AE Ch. 4.1 - Prob. 50AE Ch. 4.1 - Prob. 51MP Ch. 4.1 - Prob. 52MP Ch. 4.1 - Prob. 53DW Ch. 4.1 - Prob. 54DW Ch. 4.1 - Prob. 55DW Ch. 4.1 - Prob. 56DW Ch. 4.1 - Prob. 57RYK Ch. 4.1 - Prob. 58RYK Ch. 4.1 - Prob. 59RYK Ch. 4.1 - Prob. 60RYK Ch. 4.2 - Prob. 1AYP Ch. 4.2 - Prob. 2AYP Ch. 4.2 - Prob. 3CV Ch. 4.2 - Prob. 4CV Ch. 4.2 - Prob. 5SB Ch. 4.2 - Prob. 6SB Ch. 4.2 - Prob. 7SB Ch. 4.2 - Prob. 8SB Ch. 4.2 - Prob. 9SB Ch. 4.2 - Prob. 10SB Ch. 4.2 - Prob. 11SB Ch. 4.2 - Prob. 12SB Ch. 4.2 - Prob. 13SB Ch. 4.2 - Prob. 14SB Ch. 4.2 - Prob. 15SB Ch. 4.2 - Prob. 16SB Ch. 4.2 - Prob. 17AE Ch. 4.2 - Prob. 18AE Ch. 4.2 - Prob. 19AE Ch. 4.2 - Prob. 20AE Ch. 4.2 - Prob. 21AE Ch. 4.2 - Prob. 22DW Ch. 4.2 - Prob. 23DW Ch. 4.2 - Prob. 24DW Ch. 4.2 - Prob. 25DW Ch. 4.2 - Prob. 26DW Ch. 4.2 - Prob. 27RYK Ch. 4.2 - Prob. 28RYK Ch. 4.2 - Prob. 29RYK Ch. 4.2 - Prob. 30RYK Ch. 4.3 - Prob. 1AYP Ch. 4.3 - Prob. 2AYP Ch. 4.3 - Prob. 3AYP Ch. 4.3 - Prob. 4AYP Ch. 4.3 - Prob. 5CV Ch. 4.3 - Prob. 6CV Ch. 4.3 - Prob. 7CV Ch. 4.3 - Prob. 8CV Ch. 4.3 - Prob. 9CV Ch. 4.3 - Prob. 10CV Ch. 4.3 - Prob. 11CV Ch. 4.3 - Prob. 12CV Ch. 4.3 - Prob. 13SB Ch. 4.3 - Prob. 14SB Ch. 4.3 - Prob. 15SB Ch. 4.3 - Prob. 16SB Ch. 4.3 - Prob. 17SB Ch. 4.3 - Prob. 18SB Ch. 4.3 - Prob. 19SB Ch. 4.3 - Prob. 20SB Ch. 4.3 - Prob. 21SB Ch. 4.3 - Prob. 22SB Ch. 4.3 - Prob. 23SB Ch. 4.3 - Prob. 24SB Ch. 4.3 - Prob. 25SB Ch. 4.3 - Prob. 26SB Ch. 4.3 - Prob. 27SB Ch. 4.3 - Prob. 28SB Ch. 4.3 - Prob. 29SB Ch. 4.3 - Prob. 30SB Ch. 4.3 - Prob. 31SB Ch. 4.3 - Prob. 32SB Ch. 4.3 - Prob. 33SB Ch. 4.3 - Prob. 34SB Ch. 4.3 - Prob. 35SB Ch. 4.3 - Prob. 36SB Ch. 4.3 - Prob. 37SB Ch. 4.3 - Prob. 38SB Ch. 4.3 - Prob. 39SB Ch. 4.3 - Prob. 40SB Ch. 4.3 - Prob. 41SB Ch. 4.3 - Prob. 42SB Ch. 4.3 - Prob. 43SB Ch. 4.3 - Prob. 44SB Ch. 4.3 - Prob. 45SB Ch. 4.3 - Prob. 46SB Ch. 4.3 - Prob. 47SB Ch. 4.3 - Prob. 48SB Ch. 4.3 - Prob. 49SB Ch. 4.3 - Prob. 50SB Ch. 4.3 - Prob. 51SB Ch. 4.3 - Prob. 52SB Ch. 4.3 - Prob. 53SB Ch. 4.3 - Prob. 54SB Ch. 4.3 - Prob. 55SB Ch. 4.3 - Prob. 56SB Ch. 4.3 - Prob. 57SB Ch. 4.3 - Prob. 58SB Ch. 4.3 - Prob. 59SB Ch. 4.3 - Prob. 60SB Ch. 4.3 - Prob. 61SB Ch. 4.3 - Prob. 62SB Ch. 4.3 - Prob. 63MP Ch. 4.3 - Prob. 64MP Ch. 4.3 - Prob. 65MP Ch. 4.3 - Prob. 66MP Ch. 4.3 - Prob. 67MP Ch. 4.3 - Prob. 68MP Ch. 4.3 - Prob. 69MP Ch. 4.3 - Prob. 70MP Ch. 4.3 - Prob. 71AE Ch. 4.3 - Prob. 72AE Ch. 4.3 - Prob. 73AE Ch. 4.3 - Prob. 74AE Ch. 4.3 - Prob. 75AE Ch. 4.3 - Prob. 76AE Ch. 4.3 - Prob. 77AE Ch. 4.3 - Prob. 78AE Ch. 4.3 - Prob. 79AE Ch. 4.3 - Prob. 80AE Ch. 4.3 - Prob. 81AE Ch. 4.3 - Prob. 82AE Ch. 4.3 - Prob. 83AE Ch. 4.3 - Prob. 84AE Ch. 4.3 - Prob. 85AE Ch. 4.3 - Prob. 86AE Ch. 4.3 - Prob. 87AE Ch. 4.3 - Prob. 88AE Ch. 4.3 - Prob. 89AE Ch. 4.3 - Prob. 90AE Ch. 4.3 - Prob. 91AE Ch. 4.3 - Prob. 92AE Ch. 4.3 - Prob. 93AE Ch. 4.3 - Prob. 94DW Ch. 4.3 - Prob. 95DW Ch. 4.3 - Prob. 96DW Ch. 4.3 - Prob. 97DW Ch. 4.3 - Prob. 98DW Ch. 4.3 - Prob. 99DW Ch. 4.3 - Prob. 100DW Ch. 4.3 - Prob. 101RYK Ch. 4.3 - Prob. 102RYK Ch. 4.3 - Prob. 103RYK Ch. 4.3 - Prob. 104RYK Ch. 4.4 - Prob. 1AYP Ch. 4.4 - Prob. 2AYP Ch. 4.4 - Prob. 3AE Ch. 4.4 - Prob. 4AE Ch. 4.4 - Prob. 5AE Ch. 4.4 - Prob. 6AE Ch. 4.4 - Prob. 7AE Ch. 4.4 - Prob. 8AE Ch. 4.4 - Prob. 9AE Ch. 4.4 - Prob. 10AE Ch. 4.4 - Prob. 11AE Ch. 4.4 - Prob. 12AE Ch. 4.4 - Prob. 13AE Ch. 4.4 - Prob. 14AE Ch. 4.4 - Prob. 15AE Ch. 4.4 - Prob. 16AE Ch. 4.4 - Prob. 17AE Ch. 4.4 - Prob. 18AE Ch. 4.4 - Prob. 19AE Ch. 4.4 - Prob. 20AE Ch. 4.4 - Prob. 21AE Ch. 4.4 - Prob. 22AE Ch. 4.4 - Prob. 23AE Ch. 4.4 - Prob. 24AE Ch. 4.4 - Prob. 25AE Ch. 4.4 - Prob. 26AE Ch. 4.4 - Prob. 27MP Ch. 4.4 - Prob. 28MP Ch. 4.4 - Prob. 29MP Ch. 4.4 - Prob. 30MP Ch. 4.4 - Prob. 31DW Ch. 4.4 - Prob. 32RYK Ch. 4.4 - Prob. 33RYK Ch. 4.4 - Prob. 34RYK Ch. 4.4 - Prob. 35RYK Ch. 4.5 - Prob. 1AYP Ch. 4.5 - Prob. 2AYP Ch. 4.5 - Prob. 3SB Ch. 4.5 - Prob. 4SB Ch. 4.5 - Prob. 5SB Ch. 4.5 - Prob. 6SB Ch. 4.5 - Prob. 7SB Ch. 4.5 - Prob. 8SB Ch. 4.5 - Prob. 9SB Ch. 4.5 - Prob. 10SB Ch. 4.5 - Prob. 11SB Ch. 4.5 - Prob. 12SB Ch. 4.5 - Prob. 13SB Ch. 4.5 - Prob. 14SB Ch. 4.5 - Prob. 15SB Ch. 4.5 - Prob. 16SB Ch. 4.5 - Prob. 17SB Ch. 4.5 - Prob. 18SB Ch. 4.5 - Prob. 19SB Ch. 4.5 - Prob. 20SB Ch. 4.5 - Prob. 21SB Ch. 4.5 - Prob. 22SB Ch. 4.5 - Prob. 23MP Ch. 4.5 - Prob. 24MP Ch. 4.5 - Prob. 25MP Ch. 4.5 - Prob. 26MP Ch. 4.5 - Prob. 27MP Ch. 4.5 - Prob. 28MP Ch. 4.5 - Prob. 29MP Ch. 4.5 - Prob. 30MP Ch. 4.5 - Prob. 31MP Ch. 4.5 - Prob. 32MP Ch. 4.5 - Prob. 33AE Ch. 4.5 - Prob. 34AE Ch. 4.5 - Prob. 35AE Ch. 4.5 - Prob. 36AE Ch. 4.5 - Prob. 37AE Ch. 4.5 - Prob. 38AE Ch. 4.5 - Prob. 39DW Ch. 4.5 - Prob. 40DW Ch. 4.5 - Prob. 41DW Ch. 4.5 - Prob. 42DW Ch. 4.5 - Prob. 43DW Ch. 4.5 - Prob. 44RYK Ch. 4.5 - Prob. 45RYK Ch. 4.5 - Prob. 46RYK Ch. 4.5 - Prob. 47RYK

Knowledge Booster

The x -coordinates of the vertex of f ( x ) = a x 2 + b x + c , a ≠ 0 , is __________.

To fill: The x-coordinates of the vertex of f( x ) = a x 2 + bx + c , a ≠ 0 , is __________.

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Chapter 4 Solutions

To fill: The $x -coordinates$ of the vertex of $f (x) = a x^{2} + b x + c$ , $a \neq 0$ , is __________.