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.

Question

I need major help with this I don't understand it.

Answer 1

We know the vertex of this parabola is (-5, -7) and that it opens upward.

Given this information, the equation of the function would be y = (x+5)^2 -7.

y is at its minimum when x = -5; substituting -5 for x will make all terms drop out except for the constant -7.

 

Equation may be rewritten as y = x^2 + 10x + 18.

 

It is now apparent that y = 18 when x = 0 or -10.  y = -7 when x = -5.

 

There are other possibilities, but this is the simplest.  We didn't alter the vertical stretch of the function, but we could have.