anonymous
  • anonymous
What are the coordinates of the vertex for f(x) = 2x2 + 4x + 9? (−2, 4) (−1, 7) (1, 15) (2, 9)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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Nnesha
  • Nnesha
formula to find x coordinate of vertex \[\huge\rm x=\frac{ -b }{ 2a }\]
Nnesha
  • Nnesha
then substitute all x in f(x) equation for its value to find y-coordinate of vertex
anonymous
  • anonymous
what do i put for the a and b?

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More answers

Nnesha
  • Nnesha
a=leading coefficient b=middle term \[\huge\rm \color{reD}{A}x^2+\color{blue}{B}x+C=0\]
anonymous
  • anonymous
ok thank you
anonymous
  • anonymous
do i leave the negative sign in front of the b even when it's a positive?
Nnesha
  • Nnesha
yes b is positive but negative is in the formula so that stays there
anonymous
  • anonymous
so it would be \[x=\frac{ -4 }{ 2(2)}\]?
Nnesha
  • Nnesha
yep right
anonymous
  • anonymous
so -4/4 and i would just divide it and it would come out as -1 right?
Nnesha
  • Nnesha
yes that's x-coordinate
anonymous
  • anonymous
how do i find the y-coordinate now?
Nnesha
  • Nnesha
now to find y -coordinate substitute x for -1 \[\rm \color{reD}{x=-1}\] \[\huge\rm 2\color{reD}{x}^2+4\color{red}{x}+9=0\]
anonymous
  • anonymous
so the y-coordinate would be 3? (-1,3)?
Nnesha
  • Nnesha
mhm
Nnesha
  • Nnesha
when you take square of negative number you will get positive number
anonymous
  • anonymous
how do i do that
Nnesha
  • Nnesha
\[\huge\rm 2\color{reD}{(-1)}^2+4\color{red}{(-1)}+9=0\] now solve (-1)^2 is same as -1 times -1 = ?
anonymous
  • anonymous
so 1?
Nnesha
  • Nnesha
yes -1 times -1 = 1 (-1)^2=1 so solve \[\huge\rm 2\color{reD}{(1)}+4\color{red}{(-1)}+9=?\]
anonymous
  • anonymous
oh so (-1,7)
Nnesha
  • Nnesha
yep
anonymous
  • anonymous
could you help me out with another one
anonymous
  • anonymous
@Nnesha
Nnesha
  • Nnesha
i'll try
anonymous
  • anonymous
What is the equation of the quadratic graph with a focus of (5, −1) and a directrix of y = 1? f(x) = −one fourth (x − 5)2 + 1 f(x) = one fourth (x − 5)2 + 1 f(x) = −one fourth (x − 5)2 f(x) = one fourth (x − 5)2
anonymous
  • anonymous
@Nnesha ?
Nnesha
  • Nnesha
well not sure about this need to review this stuff hmm
Nnesha
  • Nnesha
sorry
anonymous
  • anonymous
its fine. i got it Cx thank you tho !
Nnesha
  • Nnesha
np

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