can someone help me please ? with graphs?
whats your question?
Choose the equation below that corresponds to the graph shown.
For a parabola: If you have the co-ordinates of the vertex (h,k) you can use the formula: \[\Large y=a \left( x-h \right)^2+k\]
the vertex of your graph is \(\large (-2,5)\)... so you get the equation: \[\Large y=a \left( x+2 \right)^2+5\] you just need to solve for \(\large a\) now...
how do i do that ?
you can use a second point on the graph ... whose co-ordinates you know Since this is a multiple choice question... WHAT are your choices?
you can use points \((-1,3)\) or \((0,-3)\)...
using \((x,y)=(0,-3)\) \[\Large -3=a(0+2)^2+5\] \[\Large \implies -3=4a+5\]
y = 2x2 + 8x − 3 y = −2x2 + 8x − 3 y = 2x2 − 8x − 3 y = −2x2 − 8x − 3
from the equation I wrote above : \(-3=4a+5\)..... you get \(4a=-8\) so, a=-2 \[\Large y=-2\left( x+2 \right)^2+5\]\[\Large=-2\left( x^2+4x+4 \right)+5\]\[\Large=-2\ x^2-8x-8 +5\] \[\Large\color{green}{=-2\ x^2-8x-3}\]
for multiple choice... the best method is elimination... you can eliminate A and C.... because the co-efficient of \(\large x^2\) has to be negative... because it looks like upside-down u, instead of right-side up
Join our real-time social learning platform and learn together with your friends!