# Lesson 22

Features of Parabolas

• Let’s recall what we know about parabolas.

Match the equation to the graph. Be prepared to explain your reasoning.

1. $$y = x^2+x$$
2. $$y = \text{-}x^2 - 3x$$
3. $$y = (x-1)(x+5)$$
4. $$y = x^2 + 5x +1$$

### 22.2: Features of a Quadratic Graph

1. Graph the function $$y = x^2 -10x + 16$$.
2. Find the coordinates for the
1. $$x$$-intercepts
2. $$y$$-intercept
3. vertex
3. Draw a dashed line along the line of symmetry for the graph.
4. What do you notice about the line of symmetry as it relates to the:
1. vertex
2. $$x$$-intercepts
5. Use the line of symmetry and the $$y$$-intercept to find another point on the parabola.

### 22.3: What Do You Know?

1. Write a function that is represented by a graph with $$x$$-intercepts at $$(\text-3,0)$$ and $$(1,0)$$.
1. Without graphing the function, find the $$y$$-intercept. Explain or show your reasoning.
2. Without using graphing technology, use the three points you know to sketch the graph of this function.

3. What is the $$x$$-coordinate of the vertex? Explain your reasoning.
4. Using the $$x$$-coordinate you found for the vertex, find the coordinate pair for the vertex.
1. What do you know about the coordinates of the $$y$$-intercept?
2. What do you know about the coordinates of the vertex?