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Questions and Answers
What is the formula for projectile motion?
What is the formula for projectile motion?
h(t) = \frac{1}{2}at^{2} + V_{0}t + y_{0}
What is the next step in the pattern of squares?
What is the next step in the pattern of squares?
What equation represents the number of squares after n steps?
What equation represents the number of squares after n steps?
y = n^2
Which expression represents the relationship between the step number n and the total number of small squares in the pattern?
Which expression represents the relationship between the step number n and the total number of small squares in the pattern?
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How far will the rock have fallen after 6 seconds?
How far will the rock have fallen after 6 seconds?
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Predict the distance fallen after 7 seconds.
Predict the distance fallen after 7 seconds.
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Write an equation for the function representing the distance dropped after t seconds.
Write an equation for the function representing the distance dropped after t seconds.
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What type of curve does a quadratic function produce?
What type of curve does a quadratic function produce?
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What happens to the parabola when a is positive?
What happens to the parabola when a is positive?
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What happens to the parabola when a is negative?
What happens to the parabola when a is negative?
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Noah has ___ meters of fencing to enclose a rectangular garden.
Noah has ___ meters of fencing to enclose a rectangular garden.
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Study Notes
Projectile Motion
- Projectile motion is the motion of an object influenced by gravity.
- The height of the object can be described by the following equation:
- $h(t) = \frac{1}{2}at^{2} + V_{0}t + y_{0}$
- Where:
- $h(t)$ represents height
- $t$ represents time
- $a$ represents acceleration
- $V_{0}$ represents initial velocity
- $y_{0}$ represents initial height
- Where:
- $h(t) = \frac{1}{2}at^{2} + V_{0}t + y_{0}$
- Zeros of a projectile equation represent the points where the object hits the ground (x-intercepts/roots).
Growing Steps Pattern
- The number of squares in each step follows a pattern:
- Step 1: 1 square
- Step 2: 4 squares
- Step 3: 9 squares
- The equation $y = n^2$ describes the number of squares in the pattern, where 'n' represents the step number.
Quadratic Quiz
-
Linear Functions
- General form: $Ax + By = C$
- Example: $y = 350 + 50m$
-
Exponential Functions
- General form: $y = ab^x$ or $y = a (1+r)^x$
-
Quadratic Functions
- General form: $y = ax^2 + bx + c$, $y = a(x - m)(x - n)$, or $y = a(x - h)^2 + k$
- Example: $y = x^2$
-
Parabolas
- U-shaped curves whose direction depends on the value of 'a':
- When 'a' is positive, the parabola opens upward ($∪$).
- When 'a' is negative, the parabola opens downward ($∩$).
- U-shaped curves whose direction depends on the value of 'a':
-
Vertex of a Parabola
- The minimum point of the parabola when 'a' is negative.
- The maximum point of the parabola when 'a' is positive.
Measuring a Garden
- Noah has 50 meters of fencing to create a rectangular garden.
- Students are asked to:
- Draw different rectangular garden shapes with varying lengths and widths.
- Calculate the area of each rectangle.
- Identify the length and width combination that results in the largest possible area.
- Plot the length and area values on a coordinate plane to visualize the relationship.
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Description
Test your knowledge on projectile motion and quadratic functions with this quiz. Explore the relationship between height, time, and acceleration in projectile motion, and delve into the patterns found in quadratic equations. Challenge yourself with questions on linear and exponential functions as well.
