7.10.5 Practice

Complete the following questions to practice the skills you have learned in this lesson.

1. A quadratic function $f$ is defined by $f(x)=(x-<!--\; -\; -->7)(x+3)$.

1. Without graphing, identify the $x$-intercepts of the graph of $f$.

1. $(0,-<!--\; -\; -->7),(0,3)$
2. $(0,7),(0,-<!--\; -\; -->3)$
3. $(-<!--\; -\; -->7,0),(3,0)$
4. $(7,0),(-<!--\; -\; -->3,0)$

2. Use the standard form of $(x-<!--\; -\; -->7)(x+3)$ to identify the $y$-value of the $y$-intercept of the graph of $f$.

2. Answer these questions for the equation $y=x^2-<!--\; -\; -->5x+4$.

1. What is the $y$-value of the $y$-intercept of this equation’s graph?

2. An equivalent way to write this equation is $y=(x-<!--\; -\; -->4)(x-<!--\; -\; -->1)$. What are the $x$-intercepts of this equation’s graph?

1. $(0,-<!--\; -\; -->1),(0,-<!--\; -\; -->4)$
2. $(0,1),(0,4)$
3. $(-<!--\; -\; -->1,0),(-<!--\; -\; -->4,0)$
4. $(1,0),(4,0)$

3. Noah said that if we graph $y=(x-<!--\; -\; -->1)(x+6)$, the $x$-intercepts will be at $(1,0)$ and $(-<!--\; -\; -->6,0)$. Is Noah correct?

1. No
2. Yes

4. Select two $x$-intercepts of this graph.
   
   

1. 1
2. -1
3. 3
4. -3

5. Use the standard form of $y=(x-<!--\; -\; -->2)(x-<!--\; -\; -->4)$ to identify the $y$-value of the $y$-intercept of the graph.