77.7k views
5 votes
What is the max/min of the quadratic equation in factored form: f(x) = 0.5(x+3)(x-7)? Is it a maximum or a minimum? Show your work or explain your reasoning.

1 Answer

4 votes

The given function is


f(x)=0.5(x+3)(x-7)

First, we have to find the vertex. So, let's solve the product.


\begin{gathered} f(x)=0.5(x^2-7x+3x-21) \\ f(x)=0.5(x^2-4x-21) \\ f(x)=0.5x^2-2x-10.5 \end{gathered}

Where a = 0.5 and b = -2. Let's find the horizontal coordinate of the vertex


h=-(b)/(2a)=-(-2)/(2\cdot0.5)=(2)/(1)=2

Then, we find the vertical coordinate of the vertex


k=0.5(2+3)(2-7)=0.5\cdot5(-5)=-25\cdot0.5=-12.5

The important thing about the vertex is that the coordinate k tells us the maximum or minimum. In this case, the function has a minimum at -12.5 because that's the lowest point reached by the function. The image below shows the graph

What is the max/min of the quadratic equation in factored form: f(x) = 0.5(x+3)(x-example-1
User Abdullah Bahattab
by
8.1k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories