1. Introduction to Quadratics
Mr. Daniels

2. Quadratic Equations I What is a quadratic equation?
A quadratic equation in standard form:
This exponent makes the equation quadratic
The values a, b and c are constants and have special meaning that we will explain

3. Properties of Quadratic Equations
How does a quadratic equation look?
a = 1
b = 6
c = 9
Axis of Symmetry
(divides the quadratic in half)
Determined by the formula –b/2a
x = -3
Parabola
(the graph of a quadratic)
Vertex
(the lowest or highest point of the quadratic)
Has an x and y coordinate
x coordinate is –b/2a
y coordinate is determined by substitution in the quadratic equation
Vertex (-3, 0)

4. Examples 1 & 2

5. Examples 3 & 4

6. We Do - Examples 5 & 6

7. You Do - Examples 7 & 8

8. You Do - Examples 9 & 10

9. More Properties of Quadratic Equations
What else do we know about quadratics?
Vertex is the maximum value or highest point of the quadratic
Concave Down
Concave Up
Vertex is the minimum value or lowest point of the quadratic

10. Even More Properties of Quadratic Equations
What else can learn from quadratics?
y-axis
y-intercept (same as c)
y = 12
a = 1 ; Concave Up
Crosses the x-axis twice
x = 3
x = 4
x-axis
Roots or Solutions (can be 0, 1, or 2 roots)

11. Quadratic Equations Summary
Parabola in standard form: y = ax2 + bx + c
Axis of Symmetry divides the quadratic exactly in half
Vertex is the lowest or highest point of the quadratic and has an x and a y value (x, y)
If quadratic is Concave Up it has a Minimum
If quadratic is Concave Down it has a Maximum
Roots or Solutions are the values of x where the quadratic crosses the y-axis
There can be 0, 1, or 2 roots for a quadratic
The y-intercept is y = c

12. The End