Chapter 4: Q.17 (page 247)

Graph $f (x) = 2 x^{2} - 4 x + 1$ by 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

Given information

We are given a function $f (x) = 2 x^{2} - 4 x + 1$

As the coefficient of $x^{2}$ is positive the parabola opens upward.

We find the intercepts

At x-intercept $f (x) = 0$

$2 x^{2} - 4 x + 1 = 0 x = \frac{4 \pm \sqrt{16 - 4 (2)}}{4} x = \frac{4 \pm \sqrt{16 - 8}}{4} x = \frac{4 \pm \sqrt{8}}{4} x = 0.293 o r x = 1.707$

At y-intercept $x = 0$

We have,

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

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

Find the vertex

The vertex can be given as

$x = - \frac{b}{2 a} x = - \frac{- 4}{4} x = 1$

Hence, $f (x) = 2 x^{2} - 4 x + 1 f (1) = 2 - 4 + 1 f (1) = - 1$

The coordinate of vertex is $(1, - 1)$

Plot the graph

The graph can be given as

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Graph $f (x) = 2 x^{2} - 4 x + 1$ by 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

Step by step solution

Given information

We find the intercepts

Find the vertex

Plot the graph

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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

Step by step solution

Given information

We find the intercepts

Find the vertex

Plot the graph

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Statistics

Decision Maths

Probability and Statistics

Discrete Mathematics

Logic and Functions

Study anywhere. Anytime. Across all devices.

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