quadratics review y = x 2. quadratics review this graph opens upwards y = x 2
TRANSCRIPT
Quadratics Review
y = x2
Quadratics ReviewThis graph
opens upwardsy = x2
Quadratics Review
y = x2
y = -x2
This graph opens downwards
Quadratics Review
y = x2
Quadratics Review
y = x2 y = 3x2
Quadratics Review
y = x2 y = 3x2 y = ¼ x2
Quadratics Review
Projectile Motion
Graphing and manipulating
linear and quadratic functions.
Setting up our equations:
Setting up our equations:
• In general, we take our initial x-position as x = 0
Setting up our equations:
• In general, we take our initial x-position as x = 0
• And we take GROUND LEVEL as y = 0
Setting up our equations:
• In general, we take our initial x-position as x = 0
• And we take GROUND LEVEL as y = 0
• This means that our initial y-position is often not zero!
Setting up our equations:
Initial height above ground level
Setting up our equations:
Initial height above ground level
Horizontal velocity component is constant!
Setting up our equations:
Initial height above ground level
Horizontal velocity component is constant!
Vertical velocity affected by gravity (32 ft/sec2)
Our Equations of Motion:
• In the horizontal direction:
Our Equations of Motion:
• In the horizontal direction:
x = vx t
Our Equations of Motion:
• In the horizontal direction:
x = vx t
Horizontal distance traveled
Our Equations of Motion:
• In the horizontal direction:
x = vx t
Horizontal distance traveled Horizontal velocity
Our Equations of Motion:
• In the horizontal direction:
x = vx t
Horizontal distance traveled Horizontal velocity
Time
Our Equations of Motion:
• In the vertical direction
y = -16 t2 + v0yt +y0
Our Equations of Motion:
• In the vertical direction
y = -16 t2 + v0yt +y0
Vertical position at time t
Acceleration due to gravity
Our Equations of Motion:
• In the vertical direction
y = -16 t2 + v0yt +y0
Vertical position at time t
Acceleration due to gravity
Our Equations of Motion:
• In the vertical direction
y = -16 t2 + v0yt +y0
Vertical position at time tInitial vertical velocity
Acceleration due to gravity
Our Equations of Motion:
• In the vertical direction
y = -16 t2 + v0yt +y0
Vertical position at time tInitial vertical velocity
Initial height
Acceleration due to gravity
Our Equations of Motion:
• In the vertical direction
y = -16 t2 + v0yt +y0
Vertical position at time tInitial vertical velocity
Initial height
Time
Our Equations of Motion:
• In the horizontal direction
• In the vertical direction
• Because both x and y are defined in terms of another parameter, t, we call thesePARAMETRIC EQUATIONS
y = -16 t2 + v0yt +y0
x = vx t
