Suppose the function shown below was expressed in standard form, y=ax^2+bx+c. What is the value of a? the graph shows a parabola facing downward with a vertex of (1,4) and the x intercepts are (3,0) and (-1,0) with a y intercept of (0,3)

Question

anonymous · Answer

vertex tells you it looks like 
$$y=a(x-1)^2+4$$

anonymous · Answer

now you find a.  by the way you do not need all of this information and it may very well have TOO MUCH INFORMATION.

anonymous · Answer

the vertex and one other point would do

anonymous · Answer

for example you know if x = 0 then y = 3 so put 
$$3=a(0-1)^2+4$$
$$3=a+4$$
$$a=-1$$

anonymous · Answer

does that work for any point that you plug in?

anonymous · Answer

that was enough to find a.  you do not need the other points. in fact they could even be wrong.  you cannot willy nilly specify 4 points on a parabola

anonymous · Answer

that is the point!  i do not know.  we can check them. but you can't just pick 4 points and ask for the parabola.  just like i can't say find the equation for a line between 3 points unless they are colinear

anonymous · Answer

oh alright next time i wont thanks!

anonymous · Answer

so equation is 
$$y=-(x-1)^2+4$$  and you can check if the other points work or do not

myininaya · Answer

there is alot of info here lol

anonymous · Answer

$$(-1,0)$$ works because 
$$-(-1-1)^2+4=-4+4=0$$

anonymous · Answer

ikr
you can't just say find the parabola that goes through here and here and here and here.  maybe there isn't one

anonymous · Answer

oh i understand so i shouldnt choose random points only ones that i know are correct and then i plug thwem in

anonymous · Answer

works out in this case because problem was made to work out.  but the vertex and one other point would do it

anonymous · Answer

follow what i did with vertex and one other point above.  that should convince you that we had enough information there to find the whole equation.  if other points fit that equation then they are on the graph. if they do not then they do not