can someone help me please ? with graphs?

Question

anonymous · Answer

whats your question?

anonymous · Answer

Choose the equation below that corresponds to the graph shown.

paxpolaris · Answer

For a parabola: If you have the co-ordinates of the vertex (h,k)
you can use the formula:
$$\Large y=a \left( x-h \right)^2+k$$

paxpolaris · Answer

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...

anonymous · Answer

how do i do that ?

paxpolaris · Answer

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?

paxpolaris · Answer

you can use points $(-1,3)$ or $(0,-3)$...

paxpolaris · Answer

using $(x,y)=(0,-3)$

$$\Large -3=a(0+2)^2+5$$
$$\Large \implies -3=4a+5$$

anonymous · Answer

y = 2x2 + 8x − 3 

 y = −2x2 + 8x − 3 

 y = 2x2 − 8x − 3 

 y = −2x2 − 8x − 3

paxpolaris · Answer

from the equation I wrote above : $-3=4a+5$..... you get $4a=-8$

so, a=-2

$$\Large y=-2\left( x+2 \right)^2+5$$$$\Large=-2\left( x^2+4x+4 \right)+5$$$$\Large=-2\ x^2-8x-8 +5$$
$$\Large\color{green}{=-2\ x^2-8x-3}$$

paxpolaris · Answer

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