Answer to Question #279826 in Algebra for Nickle

Question

find the maximum or minimum value or the quadratic relation y = *7 + 8x + 15 

Does the relation have a maximum or minimum value?

please show me how you got the answer

Answer 1

There is a bit inaccurate condition, i cannot understand what is the coefficient of $x^2$, so i will consider it as "a" and solve in general case, you should then put your value instead of "a" to get the answer.

So, we have quadratic function $y=ax^2+8x+15$. The gpaph of such a function is parabola with upward branches when a>0 and downward branches when a<0. So, when a>0 function has minimum and has no maximum, if a<0 then it has maximum and has no minimum. Just by the sign of "a" you can answer your second question. In both cases the extreme point is the vertex of parabola. The x-coordinate of the vertex can be found using next formula

$x_v=-{\frac b {2a}}$ , where b-coefficient of x. So, we have

$x_v=-{\frac 8 {2a}}=-{\frac 4 a}$

To find the function value we should put $x=-{\frac 4 a}$ in the equation, so

$y_v=a*(-{\frac 4 a})^2+8*(-{\frac 4 a})+15={\frac {16} a}-{\frac {32} a}+15$

So, to answer your question you should firstly determine the sign of "a", then make a corresponding conclusion about the max/min point, and find it by put your value of "a" in the $y_v$ equation.