Question

What is the relative maximum and minimum of the function? f(x) = 2x2 + 28x - 8

Answer 1

There is a minimum because the a is positive so that means the graph is upwards, the minimum would be -106!
i hope this helps

Answer 2

Minimum: y=-106. Maximum: infinite

Explanation:

The function described is a parabola, written in the form:

`f(x)=ax^2 +bx+c`

with:

`a=2\\b=28\\c=-8`

First of all, we notice that the parabola is upward, because the sign of the coefficient of the second-order term (a) is positive (in fact, a=2). Therefore, it has a minimum value of y. The x corresponding to the vertex of the parabola is given by:

`x_v=-(b)/(2a)=-(28)/(2\cdot 2)=-7`

And substituting into f(x), we find the minimum value of y:

`f(-7)=2(-7)^2+28(-7)-8=98-196-8=-106`

While the parabola has no maximum value, since it goes to infinite as x becomes larger.