1. Investigating Characteristics of Quadratic Functions
Part 1

2. What have we already seen?
We have seen equations in these forms.
1. y = x²
2. y = -3x²
3. y = -0.5x² + 4

3. Some look like these and are trinomials.
y = x² + 2x + 1 y = -x² - 3x – 6 These are quadratic equations written in standard form. The standard form of a quadratic equation is y = ax² + bx + c

4. Look at some characteristics
y = x² + 4x + 3
Y-intercept
Vertex

5. Let’s graph a couple of these and look at the vertex and y-intercept
y = x² + 2x + 1

6. Another graph…
y = x² + 2x + 6

7. And Another…
y = -3x² + 6x - 2

8. Axis of Symmetry
The axis of symmetry is the vertical line that passes through the vertex.
Now go back to the graphs
and draw in the axis of symmetry.

9. How can we find the vertex of a quadratic function without graphing it?
From standard form y = ax² + bx + c y = x² + 2x Find 2. Plug that in for x in the equation to find y. 3. Be sure to write the vertex as an ordered pair (x, y).

10. Try a few of these… Find the vertex. 1. y = 3x² + 6x - 2

11. Now let’s look at the y-intercept
What is the y-intercept of a parabola?
How do you find the y-intercept on a graph?
How would you find the y-intercept of a parabola if you don’t graph it but you have the equation?

12. More on the y-intercept
How would you find the y-intercept of a parabola if you don’t graph it but you have the equation?
Example: y = x² + 2x + 3
1. Let x = 0
2. Plug 0 in everywhere there is an x and solve for y.
3. Be sure to write the y-intercept as an ordered pair (x, y).

13. Try a few of these… Find the y-intercept 1. y = 4x² - x + 1