1. Factor and Solve Quadratic Equations
Ms. Nong

2. What is in this unit? Graphing the Quadratic Equation
Identify the vertex and intercept(s) for a parabola
Solve by taking SquareRoot & Squaring
Solve by using the Quadratic Formula
Solve by Completing the Square
Factor & Solve Trinomials (split the middle)
Factor & Solve DOTS: difference of two square
Factor GCF (greatest common factors)
Factor by Grouping

3. Parts of a Parabola
The ROOTS (or solutions) of a polynomial are its x-intercepts
Recall: The x-intercepts occur where y = 0.
Roots ~ X-Intercepts ~ Zeros
means the same

4. Solving a Quadratic The number of real solutions is at most two.
The x-intercepts (when y = 0) of a quadratic function
are the solutions to the related quadratic equation.
The number of real solutions is at most two.
Remind students that x-intercepts are found by setting y = 0 therefore the related equation would be ax2+bx+c=0. Also state that since the highest degree of a quadratic is 2, then there are at most 2 solutions. For the first graph ask “why are there no solutions?”-- there are no solutions because the parabola does not intercept the x-axis. 2nd and 3rd graph ask students to state the solutions. Additional Vocab may be itroduced: The x-intercepts are solutions, zero’s or roots of the equation.
One solution
X = 3
Two solutions
X= -2 or X = 2
No solutions

5. Vertex (h,k) Maximum point if the parabola is up-side-down
Minimum point is when the Parabola is UP
a>0
a<0

6. All parts labeled

7. Can you answer these questions?
How many Roots?
Where is the Vertex?
(Maximum or minimum)
What is the Y-Intercepts?

8. What is in this unit? Graph the quadratic equations (QE)
Solve by taking SquareRoot & Squaring
Solve by using the Quadratic Formula
Solve by Completing the Square
Factor & Solve Trinomials (split the middle)
Factor & Solve DOTS: difference of two square
Factor GCF (greatest common factors)
Factor by Grouping

9. Finding the Axis of Symmetry
When a quadratic function is in standard form
y = ax2 + bx + c,
the equation of the Axis of symmetry is
This is best read as …
‘the opposite of b divided by the quantity of 2 times a.’
Find the Axis of symmetry for y = 3x2 – 18x + 7
Discuss with the students that the line of symmetry of a quadratic function (parabola that opens up or down) is always a vertical line, therefore has the equation x =#. Ask “Does this parabola open up or down?
The Axis of symmetry is x = 3.
a = 3 b = -18

10. The x-coordinate of the vertex is 2
Finding the Vertex
The Axis of symmetry always goes through the _______. Thus, the Axis of symmetry gives us the ____________ of the vertex.
Vertex
X-coordinate
Find the vertex of y = -2x2 + 8x - 3
STEP 1: Find the Axis of symmetry
The x-coordinate of the vertex is 2
a = b = 8

11. The vertex is (2 , 5) Finding the Vertex
Find the vertex of y = -2x2 + 8x - 3
STEP 1: Find the Axis of symmetry
STEP 2: Substitute the x – value into the original
equation to find the y –coordinate of the vertex.
The vertex is (2 , 5)

12. Graphing a Quadratic Function
STEP 3: Find two other points and reflect them across the Axis of symmetry. Then connect the five points with a smooth curve. y x 3 2 y x –1 5

13. Y-intercept of a Quadratic Function
Y-axis y x
The y-intercept of a
Quadratic function can
Be found when x = 0.
The constant term is always the y- intercept

14. Example: Graph y= -.5(x+3)2+4
a is negative (a = -.5), so parabola opens down.
Vertex is (h,k) or (-3,4)
Axis of symmetry is the vertical line x = -3
Table of values x y
-1 2
-3 4
-5 2
Vertex (-3,4)
(-4,3.5)
(-2,3.5)
(-5,2)
(-1,2)
x=-3

15. Your assignment: