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Chapter 9: Q56. (page 532)

Graph the function.

y=x2鈭�2x+2

Short Answer

Expert verified

The graph of the functiony=x2鈭�2x+2 is

Step by step solution

01

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

A quadratic function, which is written in the form, y=ax2+bx+c, where,a鈮�0 is called the standard form of the quadratic function.

02

Step 2. Define the maximum or minimum point of the function y=ax2+bx+c.

The graph of the functiony=ax2+bx+c,

Opens upward and has a minimum value at x=鈭�b2a, when a>0.

Opens downward and has a maximum value at x=鈭�b2a, when a<0.

03

Step 3. Define y-intercept of the function y=ax2+bx+c.

The y-intercept of the functiony=ax2+bx+c is always at c.

04

Step 4. Plot the graph of the function y=x2−2x+2.

Compare the quadratic function y=x2鈭�2x+2with the standard quadratic function y=ax2+bx+c.

a=1,鈥�b=鈭�2,鈥�c=2

Substitutea=1andb=鈭�2in x=鈭�b2a.

x=鈭�鈭�221x=鈭�鈭�22x=鈭�鈭�1x=1

Since, a>0.

So, the graph opens upward and has a minimum value at x=1.

Since, the y-intercept is given by c.

So, the y-intercept is 2.

The graph of the function y=x2鈭�2x+2is shown below.

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