Question

How do I determine the direction a porabola opens and whether a function has a minimum or maximum

Answer 1

Answer:

the parabola opens downwards

the function has a maximum

Explanations:

For a parabola of the form:

`f(x)=ax^2\text{ + bx + c}`

If a > 0, then the parabola opens upwards and the function has a minimum

If a < 0, then the parabola opens downwards and the function has a maximum

For the function:

`f(x)=-2x^2+7x+1`

The coefficent of x², a = -2 (-ve)

Since a < 0:

the parabola opens downwards

the function has a maximum