1. Warm-Up 6 minutes Use the distributive property to find each product.
1) (x + 1)(x – 1)
2) (x + 2)(x + 9)
3) (x + 5)(4x – 7)
4) (3x – 1)(5x + 4)
5) (-x – 3)(-2x – 3)

2. 5.1 Intro to Quadratic Functions
Objectives:
Define, identify, and graph quadratic functions
Multiply linear binomials to produce a quadratic expression

3. Quadratic Function
A qudratic function is any function that can be written in the form f(x) = ax2 + bx + c, where a = 0.
The graph of a quadratic function is called a parabola.

4. Example 1
Let g(x) = (4x + 3)(x – 6). Show that g represents a quadratic function. Identify a,b, and c.
g(x) = 4x2 – 21x - 18
a = 4, b = -21, c = -18

5. Example 2
Let g(x) = (2x + 5)(3x – 2). Show that g represents a quadratic function. Identify a,b, and c.
g(x) = 6x2 + 11x - 10
a = 6, b = 11, c = -10

6. Finding the y-intercept
The value of “c” when the quadratic is in the form y = ax2 + bx + c is the y-intercept of the graph.
Ex: y = 5x2 - 3x - 8
c = -8, therefore the y-intercept is -8.

7. Example 3 Graph the quadratic function f(x) = -x2. x f(x) -2 -1 1 2 -4y
f(x) = -x2 x
f(x) -2 -1 1 2 -4 x -1 -1 -4

8. Example 3 Graph the quadratic function f(x) = -x2. y
The vertex is the maximum or minimum point of a parabola.
vertex
If the graph of a parabola is folded so that the two sides of the parabola coincide, then the fold line is the axis of symmetry. x
axis of symmetry

9. Example 3
Identify whether g(x) = -2x2 + 4x + 1 has a maximum value or a minimum value at the vertex. Then give the approximate coordinates of the vertex.
vertex
(1,3)
since the parabola opens down, it has a maximum value at the vertex

10. Minimum and Maximum Values
Let f(x) = ax2 + bx + c, where a = 0.
If a < 0, the parabola opens down and the vertex is the highest point. The y-coordinate of the vertex is the maximum value of f.
If a > 0, the parabola opens up and the vertex is the lowest point. The y-coordinate of the vertex is the minimum value of f.
a < 0
a > 0

11. Example 4
State whether the parabola opens up or down and whether it has a maximum or minimum at the vertex.
a) f(x) = -5x + 2x2 + 2
the parabola opens up, it has a minimum value at the vertex
b) g(x) = 7 – 6x – 2x2
the parabola opens down, it has a maximum value at the vertex

12. Finding the equation of the axis of symmetry and the x-coordinate of the vertex
To find the equation for the axis of symmetry and the x-coordinate of the vertex you use the equation:
Ex: y = 2x2 - 8x - 8
b = -8 & a = 2, so

13. Example 4
Find the y-intercept, equation for the axis of symmetry and the x-coordinate of the vertex.
a) f(x) = -5x + 2x2 + 2
the parabola opens up, it has a minimum value at the vertex
b) g(x) = 7 – 6x – 2x2
the parabola opens down, it has a maximum value at the vertex

14. Homework
p.290 #’s 4 – 9 “part a only”
#’s 20 – 25 “part a only”