Parabola Features
Forms of Quadratics
Converting Between Forms
Quadratics in Context
Writing Equations for Parabolas
100
Determine the y-intercept of the parabola:
(0,-8)
100
Which form would you use to find a parabola's y-intercept?
Determine the y-intercept of the parabola:
Standard Form
(0,32)
100
Convert the quadratic equation from Factored Form to Standard Form:
y=(x+5)(2x-1)
y=2x^2+9x-5
100
Nathaniel launches a toy rocket from a platform. The graph below shows the height of the rocket h in feet after t seconds. What is the rocket’s greatest height?
441 feet
100
What is the "a" value for this parabola?
a = -2
200
Determine the vertex of the parabola:
(1,-9)
200
Which form would you use to find a parabola's vertex?
Determine the vertex of the parabola:
Vertex Form!
(2,36)
200
Convert the quadratic equation from Standard Form to Factored Form:
y=x^2-3x-10
y=(x-5)(x+2)
200
Nathaniel launches a toy rocket from a platform. The graph below shows the height of the rocket h in feet after t seconds. What height was the rocket launched from?
416 feet
200
Identify the vertex and x-intercepts of this parabola:
Vertex: (-3,8)
x-intercepts: (-5,0) and (-1,0)
300
Determine the x-intercepts of the parabola:
(-2,0) and (4,0)
300
Which form would you use to find a parabola's x-intercepts?
Determine the x-intercepts of the parabola:
Factored Form!
(-4,0) and (8,0)
300
Convert the quadratic equation from Vertex Form to Standard Form:
y=-2(x-3)^2+10
y=-2x^2+12x-8
300
Nathaniel launches a toy rocket from a platform. The graph below shows the height of the rocket h in feet after t seconds. How long was the rocket in the air for?
6.5 seconds
300
Write an equation for this parabola in VERTEX FORM:
y=-2(x+3)^2+8
400
Determine the axis of symmetry of the parabola:
x = 1
400
Does this parabola open upwards or downwards?
Which form shows you?
DOWNWARDS
You can tell from any form!
400
Convert the quadratic equation from Factored Form to Standard Form:
y=7(x-1)(x+3)
7x^2+14x-21
400
Nathaniel launches a toy rocket from a platform. The graph below shows the height of the rocket h in feet after t seconds. After how many seconds did the rocket reach its maximum height?
1.25 seconds
400
Write an equation for this parabola in FACTORED FORM:
y=-2(x+5)(x+1)
500
Determine the minimum of the parabola:
-9
500
Does this parabola have a maximum or minimum?
Determine the maximum or minimum.
MAXIMUM.
The maximum is 36.
We'd use Vertex Form!
500
Convert the quadratic equation from Vertex Form to Factored Form:
y=(x+1)^2-9
y=(x-2)(x+4)
500
Nathaniel launches a toy rocket from a platform. The graph below shows the height of the rocket h in feet after t seconds. For how many seconds was the rocket's height decreasing?
5.25 seconds (from 1.25 to 6.5 seconds)
500
Write an equation for this parabola in STANDARD FORM:
y=-2x^2-12x-10