Explanation 1) Concept: Step 1: Rewrite the function f ( x ) in the form f ( x ) = ( x − h ) 2 + k using completing the square method. Step 2: Vertex of the parabola is written as ( h , k ) . find the value of h and k and write it as coordinates. Step 3: Substitute x = 0 and find the y -intercept. Step 4: Substitute y = 0 and find the x -intercept(s). Step 5: Sketch the graph by plotting the vertex, x -intercept(s) and y -intercept. Step 6: Find the axis of symmetry using the formula x = h . 2) Calculation: Let’s take f ( x ) = y to make our work simple. y = 3 x 2 + 12 x + 16 Add − 16 on both sides to isolate the x terms on the right. y − 16 = 3 x 2 + 12 x To make the coefficient of the x 2 term as 1 , factor out 3 from the terms on the right. y − 16 = 3 ( x 2 + 4 x ) Now add the square of half of the coefficient of x on both the sides. The coefficient of x is 4 . Square of half of 4 is, [ 1 2 ( 4 ) ] 2 = ( 2 ) 2 = 4 Since we are adding the 4 inside the parenthesis on the right, we are actually adding 3 ( 4 ) . So, we add 12 to the left. y − 16 + 12 = 3 ( x 2 + 4 x + 4 ) y − 4 = 3 ( x 2 + 4 x + 4 ) Now, ( x 2 + 4 x + 4 ) is a perfect square trinomial. That is, using the formula ( a + b ) 2 = a 2 + 2 a b + b 2 , x 2 + 4 x + 4 can be simplified as, x 2 + 2 ( x ) ( 2 ) + ( 2 ) 2 = ( x + 2 ) 2 So, we have, y − 4 = 3 ( x + 2 ) 2 Add 4 on both sides of the equation

Pearson eText for Beginning & Intermediate Algebra -- Instant Access (Pearson+)

6th Edition

ISBN: 9780137531929

Author: Elayn Martin-Gay

Publisher: PEARSON+

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Question

Chapter 11.6, Problem 38E

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To Answer:

Sketch the graph f(x)=3x2+12x+16. Determine whether the graph opens upward or downward and find the vertex and any intercepts.

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Chapter 11.6, Problem 37E

Chapter 11.6, Problem 39E

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Chapter 11 Solutions

Pearson eText for Beginning & Intermediate Algebra -- Instant Access (Pearson+)

Ch. 11.1 - Prob. 1G Ch. 11.1 - Prob. 2G Ch. 11.1 - Prob. 3G Ch. 11.1 - Prob. 4G Ch. 11.1 - Prob. 5G Ch. 11.1 - Prob. 6G Ch. 11.1 - Prob. 1P Ch. 11.1 - Prob. 2P Ch. 11.1 - Prob. 3P Ch. 11.1 - Prob. 4P

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To Answer: Sketch the graph f ( x ) = 3 x 2 + 12 x + 16 . Determine whether the graph opens upward or downward and find the vertex and any intercepts.

To Answer: Sketch the graph f(x)=3x2+12x+16. Determine whether the graph opens upward or downward and find the vertex and any intercepts.

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Chapter 11 Solutions

To Answer:

Sketch the graph f(x)=3x2+12x+16. Determine whether the graph opens upward or downward and find the vertex and any intercepts.