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Chapter 9: Q. 345 (page 964)

In the following exercises fx=2x2+4x+6,

Part (a): rewrite each function in fx=ax-h2+kform.

Part (b): graph it by using properties.

Short Answer

Expert verified

Part (a): The required function is fx=2x+12+4.

Part (b): The required graph is given below,

Step by step solution

01

Part (a) Step 1. Given information.

Consider the given function,

fx=2x2+4x+6

Rewrite the function in fx=ax-h2+kform by completing the square,

localid="1645119964388" fx=2x2+2x+6fx=2x2+2x+1+6-2fx=2x+12+4......(i)

02

Part (b) Step 1. Use properties to graph the function.

Identify the constants,

a=2,h=-1,k=4

Since a=2, the parabola opens upward.

The axis of symmetry is x=h. Then,

x=-1.

The vertex is h,k. Thenlocalid="1645119997516" -1,4.

Substitute x=0in the equation (i),

localid="1645120006629" f0=20+12+4=21+4=6

Therefore, y-intercept is localid="1645120028470" 0,6.

The point symmetric to localid="1645120033730" 0,6across the axis of symmetry is localid="1645120127490" -2,6.

The discriminant negative, so there are no x-intercepts.

03

Step 3. Plot the graph.

Plot the graph using the obtained information,

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