SOLUTION: A parabola has a line of symmetry x = -5. The minimum value of the quadratic function that it represents is -7. Find a possible equation of this parabola and explain how you found

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Question 1168041: A parabola has a line of symmetry x = -5. The minimum value of the quadratic function that it represents is -7. Find a possible equation of this parabola and explain how you found it.
Found 2 solutions by Boreal, MathTherapy:
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
ax^2+bx+c=0
vertex=-b/2a=-5
s0 -b=-10a
b=10a
f(-5)=-7
start with a=1 b=10
x^2+10x+c=0
when x=-5, y=7
so 25-50+c=-7 and c=18
so x^2+10x+18=0
Answer by MathTherapy(10551)   (Show Source): You can put this solution on YOUR website!

A parabola has a line of symmetry x = -5. The minimum value of the quadratic function that it represents is -7. Find a possible equation of this parabola and explain how you found it.
Vertex form of a parabolic equation: , with (h, k) being the vertex' coordinates

With the line of symmetry being - 5, and the MINIMUM value being - 7, the vertex' coordinates = (h, k) = (- 5, - 7) 

 then becomes: , and finally, the required equation: 

That's IT!! 

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