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Chapter 9: Q. 9.101 (page 942)

Find the maximum or minimum value of the quadratic function f(x)=x2-8x+12.

Short Answer

Expert verified

The minimum value of the functionf(x)=x2-8x+12 is -4.

Step by step solution

01

Step 1. Given information

Quadratic function is f(x)=x2-8x+12.

We have to find the maximum or minimum.

02

Step 2. Identify maximum or minimum

The quadratic function f(x)=ax2+bx+copens up if a>0and this function has a minimum.

In the function f(x)=x2-8x+12, a=1

since a>0, the parabola opens up and the function has a minimum.

03

Step 3. Find the vertex.

The vertex lies on the axis of symmetry x=-b2a.

x=-(-8)2(1)x=4

Find f(4).

f(4)=42-8(4)+12=16-32+12=-4

Vertex is (4,-4).

04

Step 4. Find minimum value.

Since the parabola has a minimum, the y -coordinate of the vertex is the minimum y -value of the quadratic equation. The minimum value of the quadratic is -4.

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Most popular questions from this chapter

Determine the number and type of solutions to each quadratic equation.

a)8m2-3m+6=0b)5z2+6z-2=0c)9w2+24w+16=0

Solve by using the Quadratic Formula:3y2-5y+2=0

Identify the most appropriate method to use to solve each quadratic equation.

a)8a2+3a-9=0b)4b2+4b+1=0c)5c2=125

A firework rocket is shot upward at a rate of 640 ft/sec. Use the projectile formula h=-16t2+votto determine when the height of the firework rocket will be 1200 feet.

Solve by using the Quadratic Formula:14c2-13c=112
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