Question

The graph of the function, f(x) = -2x2 + 6x -3, opens (up/down) and has a (min/max) value.

Answer 1

if your function is

`f(x) = { - 2}^(2) + 6x - 3`
then f(x) opens down, therefore has a Max.

Answer 2

f(x) opens downward and has a maximum value.

Explanation:

The given function is
`f(x)=-2x^2+6x-3`

It is a quadratic function and hence represents a parabola.

The standard form of a quadratic equation/parabola is
`y=ax^2+bx+c`

• If a>0, then the parabola opens upward and vertex is the minimum point

• If a<0, then the parabola opens downward and vertex is the maximum point

Comparing the given equation with the standard form of parabola, we get

a = -2, b = 6, c = -3

Since, a = -2 <0. Hence, the parabola opens downward and has a maximum value.