Asked by Jessica
Consider the quadratic function
f(x) = x^2 + 12x + 40. Find the vertex.
f(x) = x^2 + 12x + 40. Find the vertex.
Answers
Answered by
Reiny
complete the square,
f(x) = x^2 + 12x + 40
= x^2 + 12x + <b>36 - 36 </b> + 40
= (x+6)^2 + 4
so the vertex is (-6,4)
or
the x co-ordinate of the vertex for
f(x) = ax^2 + bx + c is -b/(2a)
so x = -12/2 = -6
sub x=-6 back into the function to find f(-6) = 36 - 72 + 40 = 4
or, if you know Calculus,
f'(x) = 2x + 12 = 0 at the vertex
2x + 12 = 0
x = -6 etc
f(x) = x^2 + 12x + 40
= x^2 + 12x + <b>36 - 36 </b> + 40
= (x+6)^2 + 4
so the vertex is (-6,4)
or
the x co-ordinate of the vertex for
f(x) = ax^2 + bx + c is -b/(2a)
so x = -12/2 = -6
sub x=-6 back into the function to find f(-6) = 36 - 72 + 40 = 4
or, if you know Calculus,
f'(x) = 2x + 12 = 0 at the vertex
2x + 12 = 0
x = -6 etc
Answered by
Jessica
Thank you! I got many more of these to do, so just wanted to make sure my first one was correct! Thanks!
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