QUADRATIC FUNCTIONS  

1. Let $f(x)=3x^2-15$. What are the roots of this quadratic function? Give exact answers.

2. Let $g(x)=x^2+6x+7$. What are the roots of this quadratic function? Give exact answers.

3. Let $h(x)=2(x-7)^2-6$. What are the roots of this quadratic function? Give exact answers.

4. The graph of a quadratic function crosses the $x$-axis at $x=8-\sqrt{11}$. Write a possible equation for this function.

   Hint (d):

   If $8−\sqrt{11}$, is an $x$-intercept, then $8+\sqrt{11}$ is also an $x$-intercept.

   Possible solution method:

   Recall that in parts (a) through (c), you let $f(x)=0$ and solved. One method here is to work backwards from that process.

   Step 1: $x=8\pm\sqrt{11}$

   Step 2:

   $x-8=\pm\sqrt{11}$

   Step 3:

   $(x-8)^2=11$

   Step 4:

   $(x-8)^2-11=0$

   Step 5:

   $y=(x-8)^2-11$