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Chapter 4: Q.17 (page 247)

Graph f(x)=2x2-4x+1by determining whether its graph opens up or down and by finding its vertex, axis of symmetry, y-intercept, and x-intercepts, if any.

Short Answer

Expert verified

The graph can be given as

Step by step solution

01

Given information

We are given a function f(x)=2x2-4x+1

As the coefficient of x2is positive the parabola opens upward.

02

We find the intercepts

At x-intercept f(x)=0

2x2-4x+1=0x=4卤16-4(2)4x=4卤16-84x=4卤84x=0.293orx=1.707

At y-intercept x=0

We have,

f(x)=2(0)-4(0)+1f(x)=1

Hence the intercepts are(0,1)(1.707,0),(0.293,0)

03

Find the vertex

The vertex can be given as

x=-b2ax=--44x=1

Hence, f(x)=2x2-4x+1f(1)=2-4+1f(1)=-1

The coordinate of vertex is(1,-1)

04

Plot the graph

The graph can be given as

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