determine whether the quadratic function shown below has a minimum or maximum, then determine the minimum or…

determine whether the quadratic function shown below has a minimum or maximum, then determine the minimum or maximum value of the function.\n\n$f(x)=-3(x + 8)(x + 5)$\n\nanswer attempt 1 out of 2\n\nthe value is.

determine whether the quadratic function shown below has a minimum or maximum, then determine the minimum or maximum value of the function.\n\n$f(x)=-3(x + 8)(x + 5)$\n\nanswer attempt 1 out of 2\n\nthe value is.

Answer

Explanation:

Step1: Find the x - coordinate of the vertex

For a quadratic function in factored form (y = a(x - r_1)(x - r_2)), the x - intercepts are (x=-8) and (x = - 5). The x - coordinate of the vertex (h=\frac{-8+( - 5)}{2}=\frac{-8 - 5}{2}=-\frac{13}{2}=-6.5)

Step2: Substitute the x - coordinate of the vertex into the function

Substitute (x=-6.5) into (f(x)=-3(x + 8)(x + 5)) [ \begin{align*} f(-6.5)&=-3(-6.5 + 8)(-6.5 + 5)\ &=-3(1.5)(-1.5)\ &=-3\times(-2.25)\ &=6.75 \end{align*} ] Since (a=-3<0), the parabola opens downwards. So the function has a maximum value.

Answer:

The maximum value is (6.75)