Explanation The graph of the quadratic equation y = a x 2 + b x + c is carried by find the ordered pair solution of the given equation by choosing some appropriate value of x . thereby finding the value of y . then plot the ordered pairs and joined the plots which gives, the graph of y = a x 2 + b x + c is a smooth curve through the plotted points. This curve is called a parabola. Find the vertex: The vertex considered by the lowest point on a parabola in opening upward and the highest point on a parabola in opening downward and the vertex formula of the parabola y = a x 2 + b x + c has x = − b 2 a . Find the intercepts: Let x = 0 and solve for y to find the y -intercepts. Let y = 0 and solve for x to find the x -intercepts. Calculation: Given, y = x 2 + 5 x + 4 Find the ordered pair’s solutions of the above equation by choosing some appropriate value for x, thereby finding the value of y. When, x = − 4 y = ( − 4 ) 2 + 5 ( − 4 ) + 4 = ( − 4 ⋅ − 4 ) + ( − 20 ) + 4 = 16 − 20 + 4 = 0 Thus, the ordered pair solution is ( − 4 , 0 ) When, x = − 3 y = ( − 3 ) 2 + 5 ( − 3 ) + 4 = ( − 3 ⋅ − 3 ) + ( − 15 ) + 4 = 9 − 15 + 4 = − 2 Thus, the ordered pair solution is ( − 3 , − 2 ) When, x = − 2 y = ( − 2 ) 2 + 5 ( − 2 ) + 4 ( − 2 ⋅ − 2 ) + ( − 10 ) + 4 = 4 − 10 + 4 = − 2 Thus, the ordered pair solution is ( − 2 , − 2 ) When, x = − 1 y = ( − 1 ) 2 + 5 ( − 1 ) + 4 = ( − 1 ⋅ − 1 ) + ( − 5 ) + 4 = 1 − 5 + 4 = 0 Thus, the ordered pair solution is ( − 1 , 0 ) When, x = 0 y = ( 0 ) 2 + 5 ( 0 ) + 4 = 0 + 0 + 4 = 4 Thus, the ordered pair solution is ( 0 , 4 ) When, x = 1 y = ( 1 ) 2 + 5 ( 1 ) + 4 = 1 + 5 + 4 = 10 Thus, the ordered pair solution is ( 1 , 10 ) When, x = 2 y = ( 2 ) 2 + 5 ( 2 ) + 4 = ( 2 ⋅ 2 ) + 10 + 4 = 4 + 10 + 4 = 18 Thus, the ordered pair solution is ( 2 , 18 ) When, x = 3 y = ( 3 ) 2 + 5 ( 3 ) + 4 = ( 3 ⋅ 3 ) + 15 + 4 = 9 + 15 + 4 = 28 Thus, the ordered pair solution is ( 3 , 28 ) When, x = 4 y = ( 4 ) 2 + 5 ( 4 ) + 4 = ( 4 ⋅ 4 ) + 20 + 4 = 16 + 20 + 4 = 40 Thus, the ordered pair solution is ( 4 , 40 ) The obtained ordered pair x y − 4 0 − 3 − 2 − 2 − 2 − 1 0 0 4 1 10 2 18 3 28 4 40 Thus, we need to plot the following ordered pair to obtain the graph

Prealgebra & Introductory Algebra (5th Edition) (What's New in Developmental Math)

5th Edition

ISBN: 9780134707631

Author: Elayn Martin-Gay

Publisher: PEARSON

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Question

Chapter 16.4, Problem 11E

To determine

To sketch:

To sketch the graph

y=x2+5x+4

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Chapter 16.4, Problem 10E

Chapter 16.4, Problem 12E

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