Chapter 9: Q2. (page 566)

Use a table of values to graph the given equation. State the domain and range.
$y = 2 x^{2} - 4 x + 3$

Short Answer

Expert verified

The graph of the given function is

The domain is $(- \infty, \infty)$ and the range is role="math" localid="1647700209891" $[1, \infty)$ .

Step by step solution

Step 1. Define the standard form of the quadratic function.

A quadratic function, which is written in the form, $y = a x^{2} + b x + c$ , where, $a \neq 0$ is called the standard form of the quadratic function.

Step 2. Define the domain and range of a function.

The domain is the set of all of the possible values of the independent variable $x$ .

The range is the set of all the possible values of the dependent variable $y$ .

Step 3. Calculate the table of values for the function y=2x2−4x+3.

$x$	$y$
$- 2$	19
$- 1$	9
0	3
1	1
2	3

Step 4. Use the table of values to graph the function y=2x2−4x+3.

Graph the ordered pairs from the table and connect them to create a smooth curve.

Step 5. State the domain and range for function y=2x2−4x+3.

Observe the graph.

The parabola extends to infinity.

So, the domain is $(- \infty, \infty)$ .

The minimum value of the function is 11.

So, the range is $[1, \infty)$ .

Therefore, the domain is $(- \infty, \infty)$ and the range is $[1, \infty)$ .

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Use a table of values to graph the given equation. State the domain and range.
$y = 2 x^{2} - 4 x + 3$

Short Answer

Step by step solution

Step 1. Define the standard form of the quadratic function.

Step 2. Define the domain and range of a function.

Step 3. Calculate the table of values for the function y=2x2−4x+3.

Step 4. Use the table of values to graph the function y=2x2−4x+3.

Step 5. State the domain and range for function y=2x2−4x+3.

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Use a table of values to graph the given equation. State the domain and range.y=2x2−4x+3

Short Answer

Step by step solution

Step 1. Define the standard form of the quadratic function.

Step 2. Define the domain and range of a function.

Step 3. Calculate the table of values for the function y=2x2−4x+3.

Step 4. Use the table of values to graph the function y=2x2−4x+3.

Step 5. State the domain and range for function y=2x2−4x+3.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

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Study anywhere. Anytime. Across all devices.

Use a table of values to graph the given equation. State the domain and range.
$y = 2 x^{2} - 4 x + 3$