Thursday, June 11, 2015

College Algebra, Chapter 4, 4.1, Section 4.1, Problem 14

A quadratic function f(x)=x22x+2.

a.) Find the quadratic function in standard form.


f(x)=x22x+2f(x)=1(x22x)+2Factor out 1 from x-termsf(x)=1(x22x+1)+2(1)(1)Complete the square: add 1 inside parentheses, subtract (1)(1) outsidef(x)=(x1)2+1Factor and simplify


The standard form is f(x)=(x1)2+1.

b.) Find its vertex and its x and y-intercepts.

By using f(x)=a(xh)2+k with vertex at (h,k).

The vertex of the function f(x)=(x1)2+1 is at (1,1).


Solving for x-interceptSolving for y-interceptWe set f(x)=0, thenWe set x=0, then0=(x1)2+1Subtract 1y=(01)2+1Substitute x=01=(x1)2Take the square rooty=1+1Simplify±1=x1y=2x-intercept does not exist


c.) Draw its graph.

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