The provided parabola is the the kind ,
You are watching: What is the line of symmetry for the parabola whose equation is y = x2 + 10x + 25?
So, vertex of the provided parabola is , in ~ (-5,0).
The meaning of term heat of symmetry,is the line which divides the parabola in two equal halves.
Drawing the parabola,and recognize the heat of symmetry,which deserve to be derived by illustration a heat parallel to y axis, passing through (-5,0).
So, the equation of heat is : x= -5
The heat of the opposite passes v the peak of the parabola. The x coordinate that the crest is discovered with the formula x=−b2a for the equation that the form y=ax2+bx+c.
In this example, a=1, b=10 and c=25
Because the line of the contrary passes with the vertex, the equation of the line is x=−5.
In bespeak to carry out this, usage the basic formula x = -b/2a, where a and b space taken directly from the equation for the parabola. A = 1 and also b = 10, so your line of the opposite equation is x = -10/2(1) or x = -5, i m sorry is additionally the x coordinate of the vertex. The long means that will certainly tell you the y coordinate of the vertex would be to placed it into vertex kind by completing the square. Yet not important here together you are just being asked for the line of symmetry. If you room told to uncover the collaborates of the peak this simplified equation will certainly not work.
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The line because that axis the symmetry deserve to be found with 2 ways1 long way (finding x worth of vertex)2. Short way (finding axis that symmetry using equation)1. Long waycomplete the squarey=x^2+10x+25take 1/2 of lienar coefnent and also square it10/2=5, 5^2=25intersting, we have actually 25 alreadyfactor perfect squarey=(x+5)^2in formy=a(x-h)^2+kvertex is (h,k)axis of symmetry is x=hsoy=1(x-(-5))^2+0axis of the opposite is x=-5short wayfory=ax^2+bx+cthe x worth of the peak or the axis of symmetry is -b/(2a)giveny=1x^2+10x+25a=1b=10-b/(2a)=-10/(2*1)=-10/2=-5the axis of symmety is x=-5
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