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| x | y |
|---|---|
| - 1 | 0 |
| 0 | - 3 |
| 1 | - 4 |
| 2 | - 3 |
| 3 | 0 |
Graph:
Graph:
Time: 4 seconds.
| x | x^2-2x-3 | y |
|---|---|---|
| - 1 | ( - 1)^2-2( - 1)-3 | 0 |
| 0 | 0^2-2( 0)-3 | - 3 |
| 1 | 1^2-2( 1)-3 | - 4 |
| 2 | 2^2-2( 2)-3 | - 3 |
| 3 | 3^2-2( 3)-3 | 0 |
Now we can draw the graph.
y=a(x-2)(x-5)
x= 3.5, y= - 2
Subtract term
Multiply
LHS * (- 1)=RHS* (- 1)
Rearrange equation
.LHS /2.25.=.RHS /2.25.
a/b=a * 4/b * 4
A possible equation is y= 89(x-2)(x-5).
y=x^2+(a+b)x+ab
⇕
y=(x+a)(x+b)
From the equation, we can identify what this sum and product must be.
cccccc
y&=&x^2 & + & 8 & -7pt x & + & 7
y&=&x^2 & + & (a+b) & -7pt x & + & ab
y= 0
Use the Zero Product Property
(I): LHS-1=RHS-1
(II): LHS-7=RHS-7
The function has two x-intercepts at x=- 1 and x=- 7. Since this is a second degree equation, we can find the vertex by calculating the average of these intercepts. average: - 1+(- 7)/2=- 4 When we know the vertex x-value we can find its y-value by substituting x=4 into the function.
x= -4
Calculate power
a(- b)=- a * b
Add and subtract terms
The vertex is at (- 4,- 9). With this information, we can draw the graph.
y= 0
Factor out 16x
.LHS /16.=.RHS /16.
Use the Zero Product Property
(II): LHS-8=RHS-8
(II): LHS * (- 1)=RHS* (- 1)
The maximum height is 256 feet.
