Question

Without using the vertex formula or graphing calculator, find the vertex of 2x^2+5x+7. Show your work.

Answer 1

Use differentiation to find the minimum:

\[\frac{ d }{ dx } 2x^2+5x+7\]
\[4x+5\]
Set 4x+5=0 and find the x coordinate of the vertex. You would get -5/4. Now plug that into the original equation. You would get 31/8. Your vertex is \[(\frac{ -5 }{ 4 }, \frac{ 31 }{ 8 })\]

Answer 2

@Evo did you understand what @Ferredoxin4 is showing you? Are you currently taking a calculus course?

Answer 3

Yea I get it just couldn't think of what they meant

Answer 4

My question is, What course are you currently taking

Answer 5

precalc

Answer 6

Yes but is differentiation something that your instructor has gone over with you in class.

Answer 7

Yes it's just that I didn't realize they were asking me to differentiate I had a brain fart lol

Answer 8

I doubt if they were asking you to do differentiation in pre-calculus. There's a non-calculus way to find the vertex which is what is more appropriate for a pre-calculus course.

Answer 9

Oh the unit was prepartion for calculus so they told me to use differentiation but whats the appropriate way

Answer 10

The other way to do this is to write the expression in the form a(x - h)^2 + k

Answer 11

(h,k) would be the vertex

Answer 12

ohh yess we can also do that

Answer 13

Looking at the way the question was asked, I'm 99% certain this is the way your instructor was expecting you to do it. If you were expected to perform differentiation, I'm certain this would have been mentioned in the problem beforehand.

Answer 14

Oh okay I see