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Chapter 10: Q 320. (page 1238)

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

y=-3x2+12x-10

Short Answer

Expert verified

The maximum value is 2.

Step by step solution

01

Step 1. Given information.

The given information is:

y=-3x2+12x-10

02

Step 2. Find the maximum value of the function.

y=ax2+bx+cy=-3x2+12x-10

The value of coefficient ais negative therefore we can say that the parabola opens down.

The axis of symmetry is the line x=-b2a.

Substitute the values of a, and binto the equation.

x=-122-3=2

Therefore, the axis of symmetry is x=2.

The vertex is on the line of symmetry, so its x-coordinate will be x=2.

Now substitute the value of xinto the equation,

y=-322+122-10=-12+24-10=2

Therefore, the vertex is (2,2).

The maximum value of the given function is 2 and it occurs at the value of xas 2.

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