Answer:
Minimum: y=-106. Maximum: infinite
Step-by-step explanation:
The function described is a parabola, written in the form:
[tex]f(x)=ax^2 +bx+c[/tex]
with:
[tex]a=2\\b=28\\c=-8[/tex]
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:
[tex]x_v=-\frac{b}{2a}=-\frac{28}{2\cdot 2}=-7[/tex]
And substituting into f(x), we find the minimum value of y:
[tex]f(-7)=2(-7)^2+28(-7)-8=98-196-8=-106[/tex]
While the parabola has no maximum value, since it goes to infinite as x becomes larger.
