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The parabola \(y = ax^2 + bx + c\) is graphed below. Find \(a \cdot b \cdot c\). (The grid lines are one unit apart.)

 

0.1) { TicksArrx.push(i);} } for(i=ybottom+ystep; i 0.1) { TicksArry.push(i);} } if(usegrid) { xaxis(BottomTop(extend=false), Ticks("%", TicksArrx ,pTick=gray(0.22),extend=true),p=invisible);//,above=true);yaxis(LeftRight(extend=false),Ticks("%", TicksArry ,pTick=gray(0.22),extend=true), p=invisible);//,Arrows);} if(useticks) { xequals(0, ymin=ybottom, ymax=ytop, p=axispen, Ticks("%",TicksArry , pTick=black+0.8bp,Size=ticklength), above=true, Arrows(size=axisarrowsize));yequals(0, xmin=xleft, xmax=xright, p=axispen, Ticks("%",TicksArrx , pTick=black+0.8bp,Size=ticklength), above=true, Arrows(size=axisarrowsize));} else { xequals(0, ymin=ybottom, ymax=ytop, p=axispen, above=true, Arrows(size=axisarrowsize));yequals(0, xmin=xleft, xmax=xright, p=axispen, above=true, Arrows(size=axisarrowsize));} };rr_cartesian_axes(-7,1,-3,7);real f(real x) {return 1/2*x^2 + x + 3/2;} draw(shift((-2,-3))*graph(f,-5,3,operator ..), red);[/asy]" src="/api/ssl-img-proxy?src=https%3A%2F%2Flatex.artofproblemsolving.com%2F3%2Fd%2Fc%2F3dcbfd37344accf75039423aaee0e135a89dc16a.png">

 Apr 12, 2020
 #1
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+1

hmm... the image isnt working... let me try again:

 

 Apr 12, 2020
 #2
avatar+23552 
+1

There are two 'zeroes' at   x = -1  and -5      these are the roots

 

so the equation becomes:

 

(x+1)(x+5) = 0

x^2 +6x +5 = 0         y = x^2+6x+5   has the same roots , but not the same vertex

 

the vertex needs to be shifted up    

 

the y value needs to be -2   at x = -3

 

(-3)^2 + 6(-3) + 5 = -4        Needs to be -2         multiply all of the coefficients by 1/2

 

1/2x^2 + 3x + 2.5     then when x = -3

   4.5    + -9  +  2.5  = -2

 

y =  1/2x^2 + 3x + 2.5 

 Apr 12, 2020
 #3
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0

Thank you! But whats the answer for a*b*c?

Guest Apr 12, 2020
 #4
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The final answer is 15/8.

Guest Apr 12, 2020
 #5
avatar+23552 
+1

You're kidding right????????????cheeky

 

y =     a x^2 +bx + c

y =  1/2x^2 + 3x + 2.5       

ElectricPavlov  Apr 12, 2020
edited by ElectricPavlov  Apr 12, 2020
 #6
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0

ok thank you kind millenial

Guest Apr 12, 2020

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