# Quadratic Function - PowerPoint by Xu34Z7

VIEWS: 13 PAGES: 17

• pg 1
```									Name:
Date:
Topic: Solving & Graphing Quadratic Functions
Warm-Up:
Factor
1. 49p2 – 100

2. 6d4 + 4d3 – 6d2 – 4d

Solve for x:
3. 2x2 + 13x + 6
(y = ax 2 + bx + c)
Vocabulary:

2. Parabola = the graph of a
shaped curved.

3. Axis of Symmetry – divide the
graph into two halves

The line of symmetry ALWAYS
passes through the vertex.

Continue
4. Vertex
• Minimum – lowest point
of the parabola
• Maximum – the highest
point of the parabola.     y

Vertex
Maximum

x

Vertex
Minimum
y = x2
   a = 1, b = 0, c = 0
   Minimum point (0,0)
   Axis of symmetry      y=x2
x=0
Finding the Line of Symmetry

When a quadratic function is in   For example…
standard form
Find the line of symmetry of
y=   ax2   + bx + c,             y = 3x 2 – 18x + 7
The equation of the line of
symmetry is                       Using the formula…
b
x                 x  18  18  3
2a                 2 3 6

Thus, the line of symmetry is x = 3.
Finding the Vertex
We know the line of symmetry                    y = –2x 2 + 8x –3
always goes through the vertex.
STEP 1: Find the line of symmetry
Thus, the line of symmetry
gives us the x – coordinate of                 x  b  8  8  2
2a 2(2) 4
the vertex.
STEP 2: Plug the x – value into the
original equation to find the y value.
To find the y – coordinate of the
vertex, we need to plug the x –                   y = –2(2)2 + 8(2) –3
value into the original equation.
y = –2(4)+ 8(2) –3

y = –8+ 16 –3
y=5

Therefore, the vertex is (2 , 5)
A Quadratic Function in Standard Form
Let's Graph ONE! Try …           y

y = 2x 2 – 4x – 1
STEP 1: Find the line of symmetry

STEP 2: Find the vertex

x
STEP 3: Find the y-intercept
when x = 0.

STEP 4: Find two other points
and reflect them across the line
of symmetry. Then connect the
five points with a smooth curve.
A Quadratic Function in Standard Form
y
y=   2x2   – 4x – 1

x
What happen if we change
the value of a and c ?

y=3x2        y=4x2+3

y=-3x2       y=-4x2-2
Conclusion
(y = ax 2+bx+c)

   When a is positive,      the graph concaves
downward.
   When a is negative,      the graph concaves
upward.
   When c is positive       the graph moves up.
   When c is negative       the graph moves
down.
Other Methods

   By factoring

   By using the
quadratic formula      b  b  4ac
2
x
2a
Factoring Example

   X2 - 2x = 0
   Factor in order to      y=x2-2x
solve the equation
yourself does the
function have a GCF.
   Find the x intercept.
   Two solutions, x=0
and x=2.
Find the Solutions

y=x2-4
y=x2+2x-15

y=-x2+5

y=-x2-1
Find the solutions

y=-x2+4x-1
Group Work:                  Page 544 – 545
Group 1:   Group 3:   Group 5:      Group 7:
#7, #20    #9, #22    #11, #24      #13, #28

Group 2:   Group 4:   Group 6:      Group 8:
#8, #21    #10, #23   #12, #25      #14, #30

Independent Work:
Page 538 (8, 10)
Page 546 (43)
Page 549 (a, b, c)
HLA#1:

Page 538 (7, 8)
Page 544 (2, 3, 4)

```
To top