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Chapter 9: Q. 494 (page 985)

In the below exercise, find the minimum or maximum value.

y=7x2+14x+6

Short Answer

Expert verified

The equationy=7x2+14x+6has a minimum value of-1atx=-1.

Step by step solution

01

Step 1. Given Information.

We have:

y=7x2+14x+6

02

Step 2. Find and maximum or minimum value.

The鈥�vertex鈥�of鈥�an鈥�up-down鈥�facing鈥�parabola鈥�of鈥�the鈥�form鈥�y=ax2+bx+c鈥�is鈥�xv=-b2a

The鈥�parabola鈥�params鈥�are:a=7,鈥�b=14,鈥�c=6xv=-b2axv=-142路鈥�7xv=-1

Substitute xv=-1in the original value to find yv:

yv=-1Therefore鈥�the鈥�parabola鈥�vertex鈥�is-1,鈥�-1If鈥�a<0,鈥�then鈥�the鈥�vertex鈥�is鈥�a鈥�maximum鈥�valueIf鈥�a>0,鈥�then鈥�the鈥�vertex鈥�is鈥�a鈥�minimum鈥�valuea=7Minimum-1,鈥�-1

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