anonymous 4 years ago consider the following quadratic function...k(x)=(x-6)..find the vertex of this function

1. anonymous

2. anonymous

is (x-6) raised to the 2nd power?

3. anonymous

no...it's not on the problem...that's how it's worded

4. anonymous

k(x)=x-6 is a line

5. anonymous

I have the answer..I just don't understand how to do the problem...the answer is (6,0)

6. anonymous

Well, I'm going to assume it is k(x)=(x-6)^2 Expand: x^2-12x+36 The vertex of a parabola written in the for ax^2+bx+c is: $(-\frac{b}{2a},f(-\frac{b}{2a})$ $(\frac{12}{2},f(\frac{12}{2}))=(6,f(6))=(6,0)$

7. anonymous

looks good....worked it out..now quick question...why is f(6)=0?

8. anonymous

f(6)=6^2-12(6)+36=36-72+36=0

9. anonymous

or in the original form, f(x)=(x-6)^2 f(6)=(6-6)^2=0^2=0

10. anonymous

makes sense now thank you