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Graph the function.

y=2x28x+2

Short Answer

Expert verified

The graph of the functiony=2x28x+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,a0 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=b2a, when a>0.

Opens downward and has a maximum value at x=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 atc.

04

Step 4. Plot the graph of the function y=−2x2−8x+2.

Compare the quadratic function y=2x28x+2with the standard quadratic function y=ax2+bx+c.

a=2,b=8,c=2

Substitutea=2andb=8in x=b2a.

x=822x=84x=2x=2

Since, a<0.

So, the graph opens downward and has a maximum value at x=2.

Since, the y-intercept is given by c.

So, the y-intercept is 2.

The graph of the function y=2x28x+2is shown below.

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