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Chapter 3: Q. 48 (page 156)

Determine the quadratic function whose graph is given.

Short Answer

Expert verified

The quadratic function whose graph is given is f(x)=(x-2)2+1or f(x)=x2-4x+5.

Step by step solution

01

Step 1. Given information.

The given graph is:

02

Step 2. Determine the equation.

The vertex is (2,1), so h=2and k=1. Substitute these values into equation f(x)=a(x-h)2+k.

f(x)=a(x-2)2+1

To determine the value of a, we use the fact that f(0)=5(the y-intercept).

5=a(0-2)2+15-1=4a4=4a1=a

Substitute a=1in f(x)=a(x-2)2+1.

f(x)=1(x-2)2+1f(x)=(x-2)2+1f(x)=x2-4x+4+1f(x)=x2-4x+5

03

Step 3. Conclusion.

The quadratic function whose graph is given is f(x)=(x-2)2+1or f(x)=x2-4x+5.

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