Algebra 2
Algebra 2
1st Edition
ISBN: 9780078884825
Author: McGraw-Hill/Glencoe
Publisher: Glencoe/McGraw-Hill School Pub Co
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Chapter 10.2, Problem 1CYP
To determine

To write: The equation in standard form and identify the vertex, axis of symmetry and direction of opening of the parabola.

Expert Solution & Answer
Check Mark

Answer to Problem 1CYP

The standard equation is x=3(y+2)2+30 , vertex is (30,2) , axis of symmetry is y=2 and parabola opens towards left.

Explanation of Solution

Given:

The given equation is y=4x2+16x+34.

Calculation:

Rewrite the given quadratic equation in the standard form by completing the square.

  y=4x2+16x+34=4(x2+4x+4)16+34=4(x+2)2+18

Therefore, the standard form of the given quadratic equation is y=4(x+2)2+18.

Compare the equation y=4(x+2)2+18 with the standard equation y=a(xh)2+k.

  a=4h=2k=18

Therefore, the vertex of the given equation is (2,18).

Axis of symmetry will be given shown below.

  y=k=18

Therefore, the axis of symmetry is y=18.

As it is found that the value of a=4 is positive so so by definition the parabola opens upward.

Therefore, the standard equation is y=4(x+2)2+18 , vertex is (2,18) , axis of symmetry is y=18 and parabola opens upward.

Chapter 10 Solutions

Algebra 2

Ch. 10.1 - Prob. 7CYUCh. 10.1 - Prob. 8CYUCh. 10.1 - Prob. 9CYUCh. 10.1 - Prob. 10PPSCh. 10.1 - Prob. 11PPSCh. 10.1 - Prob. 12PPSCh. 10.1 - Prob. 13PPSCh. 10.1 - Prob. 14PPSCh. 10.1 - Prob. 15PPSCh. 10.1 - Prob. 16PPSCh. 10.1 - Prob. 17PPSCh. 10.1 - Prob. 18PPSCh. 10.1 - Prob. 19PPSCh. 10.1 - Prob. 20PPSCh. 10.1 - Prob. 21PPSCh. 10.1 - Prob. 22PPSCh. 10.1 - Prob. 23PPSCh. 10.1 - Prob. 24PPSCh. 10.1 - Prob. 25PPSCh. 10.1 - Prob. 26PPSCh. 10.1 - Prob. 27PPSCh. 10.1 - Prob. 28PPSCh. 10.1 - Prob. 29PPSCh. 10.1 - Prob. 30PPSCh. 10.1 - Prob. 31PPSCh. 10.1 - Prob. 32PPSCh. 10.1 - Prob. 33PPSCh. 10.1 - Prob. 34PPSCh. 10.1 - Prob. 35PPSCh. 10.1 - Prob. 36PPSCh. 10.1 - Prob. 37PPSCh. 10.1 - Prob. 38PPSCh. 10.1 - Prob. 39PPSCh. 10.1 - Prob. 40PPSCh. 10.1 - Prob. 41PPSCh. 10.1 - Prob. 42HPCh. 10.1 - Prob. 43HPCh. 10.1 - Prob. 44HPCh. 10.1 - Prob. 45HPCh. 10.1 - Prob. 46HPCh. 10.1 - Prob. 47STPCh. 10.1 - Prob. 48STPCh. 10.1 - Prob. 49STPCh. 10.1 - Prob. 50STPCh. 10.1 - Prob. 51SRCh. 10.1 - Prob. 52SRCh. 10.1 - 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