### Home > PC3 > Chapter 4 > Lesson 4.1.1 > Problem4-7

4-7.

Set the right side of each equation equal to $0$ and solve for $x$.

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.

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

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: $x=8\pm\sqrt{11}$

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

$(x-8)^2=11$

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

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