Answered

Westonci.ca is the ultimate Q&A platform, offering detailed and reliable answers from a knowledgeable community. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.

F(x) =2x^2+12x-6 Does this function have a minimum or maximum value? What is this minimum or maximum value?

Sagot :

Let's compare the given function with the model for a quadratic equation:

[tex]\begin{gathered} f(x)=ax^2+bx+b \\ a=2,b=12,c=-6 \end{gathered}[/tex]

Since the value of a is positive, the parabola has its concavity upwards, and the function has a minimum value.

The minimum value can be found calculating the y-coordinate of the vertex:

[tex]\begin{gathered} x_v=-\frac{b}{2a}=-\frac{12}{4}=-3 \\ \\ y_v=2\cdot(-3)^2+12\cdot(-3)-6 \\ y_v=2\cdot9-36-6^{} \\ y_v=-24 \end{gathered}[/tex]

Therefore the minimum value is -24.

We appreciate your visit. Hopefully, the answers you found were beneficial. Don't hesitate to come back for more information. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.