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Chapter 9: Q. 495 (page 985)

In the following exercises, find the minimum or maximum value.

y=-3x2+12x-10

Short Answer

Expert verified

The equation has a maximum value2atx=2.

Step by step solution

01

Step 1. Given information.

We have:

y=-3x2+12x-10

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=-3,鈥�b=12,鈥�c=-10xv=-b2axv=-122-3xv=2

Plug xv=2in the original function to find yv:

yv=2Therefore鈥�the鈥�parabola鈥�vertex鈥�is2,鈥�2If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=-3Maximum2,鈥�2

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