For this case we have that by definition, the equation of the line in the slope-intersection form is given by:
Where:
m: It is the slope of the line
b: It is the cut-off point with the y axis
We have the following points through which the line passes:
We find the slope of the line:
Thus, the equation of the line is of the form:
We substitute one of the points and find b:
Finally, the equation is:
Answer:
So the easiest method to find the vertex (the minimum in this case) to do this is to find the axis of symmetry, then plug it into the function.
Firstly, the equation to find the axis of symmetry is , with b = x coefficient and a = x^2 coefficient. The equation equation can be solved as such:
Since the vertex falls on the axis of symmetry, we know that the x-coordinate of the vertex is -2.5. Now to solve for the y-coordinate, plug in x with -2.5 and solve as such:
Now putting it all together, our minimum value (vertex) is (-2.5,-12.25).
