5.1: Introduction to quadratic functions

 

1. Find the zeros of \(Q(s)=3 s^2-3 s-60\) by factoring. Show your work.

 

 

 

2. Find the zeros of \(Q(x)=5 x-x^2+3\) using the quadratic formula. Show your work.

 

 

 

 

3. First, sketch a graph of a quadratic function which has all the following properties: \(y\)-intercept equal to -6, zeros at \(x=-2\) and \(x=3\). Then, write a formula for this quadratic function.

 

 

 

 

4. Without a calculator, graph \(y=3 x^2-16 x-12\) by factoring and plotting zeros. Then check your answer using Desmos.

 

 

 

 

 

5. Find a formula for the quadratic functions described below.

1. A \(y\)-intercept of \(y=7\) and the only zero at \(x=-2\).
2.  

 

 

 

 

 

6. A ball is thrown into the air. Its height (in feet) \(t\) seconds later is given by \(h(t)=80 t-16 t^2\).

1. Evaluate and interpret \(h(2)\).
2. Solve the equation \(h(t)=80\). Interpret your solutions and illustrate them on a graph of \(h(t)\).
    

 

 

---