Given the function, = − 1/10 ^2 − 5 − 1/4 ; determine the coordinates of the vertex. does this function have a maximum or minimum value ? Explain how you can tell.

Question

this is a quadratic function.

Answer 1

Assuming the function is y = -1/10 x^2 -5x -1/4 -----------------------(1)

Vertex of a parabola of the form ax^2 +bx +c is (-b/2a,y)

so, x coordinate of vertex = - (-5)/ {2(-1/10)} = -25

putting the value of x-coordinate of vertex in equation (1) we get: y = 62.25

So the vertex = (-25,62.25)

The parabola has maximum at (-25,62.25) and no minimum value. It has a maximum value at vertex because a<0 and no minimum value because it has no lower bound.