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What is the equation of the quadratic function in standard form with zeros of -3 and 1, passing through the point (-1, -7)?
What is the equation of the quadratic function in standard form with zeros of -3 and 1, passing through the point (-1, -7)?
What is the equation of the quadratic function in vertex form with a vertex of (-2, 3) and passing through the point (-1, 6)?
What is the equation of the quadratic function in vertex form with a vertex of (-2, 3) and passing through the point (-1, 6)?
What is the equation of the quadratic function in factored form which has zeros of -2 and 4 and a y-intercept of -3?
What is the equation of the quadratic function in factored form which has zeros of -2 and 4 and a y-intercept of -3?
What is the equation of the quadratic function in vertex form, with a maximum at (4, -2) and congruent to y = 2x²?
What is the equation of the quadratic function in vertex form, with a maximum at (4, -2) and congruent to y = 2x²?
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What is the equation of the quadratic function in standard form with a vertex of (-4, 1) and a y-intercept of -5?
What is the equation of the quadratic function in standard form with a vertex of (-4, 1) and a y-intercept of -5?
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What is the step pattern of a parabola with the equation y = 2(x - 3)^2 + 1?
What is the step pattern of a parabola with the equation y = 2(x - 3)^2 + 1?
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What is the optimal value of the quadratic relation y = -x^2 + 4x + 5?
What is the optimal value of the quadratic relation y = -x^2 + 4x + 5?
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Which of the following is NOT a characteristic of the axis of symmetry of a parabola?
Which of the following is NOT a characteristic of the axis of symmetry of a parabola?
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What is the y-intercept of the quadratic relation y = 2x^2 - 3x + 1?
What is the y-intercept of the quadratic relation y = 2x^2 - 3x + 1?
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If the vertex of a parabola is located at the point (2, -3), what is the equation of the axis of symmetry?
If the vertex of a parabola is located at the point (2, -3), what is the equation of the axis of symmetry?
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What is the domain of the quadratic relation y = x^2 - 4x + 3?
What is the domain of the quadratic relation y = x^2 - 4x + 3?
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What are the zeros of the quadratic relation y = x^2 - 4?
What are the zeros of the quadratic relation y = x^2 - 4?
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If a parabola opens downwards, what can you conclude about the coefficient of the squared term in its equation?
If a parabola opens downwards, what can you conclude about the coefficient of the squared term in its equation?
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What is the quadratic equation that models the number of imported cars sold in Newfoundland between 2003 and 2007?
What is the quadratic equation that models the number of imported cars sold in Newfoundland between 2003 and 2007?
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Using the quadratic equation, how many imported cars would you expect to be sold in 2008?
Using the quadratic equation, how many imported cars would you expect to be sold in 2008?
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What does the model predict for the number of imported cars sold in 2006?
What does the model predict for the number of imported cars sold in 2006?
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In the quadratic inequality 𝑥 2 − 4 ≤ 0, what is the interval where the graph of the quadratic relation is on or below the x-axis?
In the quadratic inequality 𝑥 2 − 4 ≤ 0, what is the interval where the graph of the quadratic relation is on or below the x-axis?
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What is the factored form of the quadratic inequality 𝑥 2 − 4 ≤ 0?
What is the factored form of the quadratic inequality 𝑥 2 − 4 ≤ 0?
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Using an interval chart to solve the quadratic inequality 𝑥 2 − 4 ≤ 0, where does the product of the factors (𝑥 + 2) and (𝑥 − 2) change signs?
Using an interval chart to solve the quadratic inequality 𝑥 2 − 4 ≤ 0, where does the product of the factors (𝑥 + 2) and (𝑥 − 2) change signs?
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In the context of solving quadratic inequalities, what does the term 'interval' refer to?
In the context of solving quadratic inequalities, what does the term 'interval' refer to?
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What is the main difference between solving a quadratic equation and a quadratic inequality?
What is the main difference between solving a quadratic equation and a quadratic inequality?
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A campground charges $20.00 to camp for one night and averages 56 people each night. If they decrease the price by $1.00, the number of campers increases by 7. What is the price that will maximize nightly revenue?
A campground charges $20.00 to camp for one night and averages 56 people each night. If they decrease the price by $1.00, the number of campers increases by 7. What is the price that will maximize nightly revenue?
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A toy rocket is launched with an initial velocity of 180 m/s and its height is modeled by h = -5t² + 180t, where t is the time in seconds. How long will the rocket stay above a height of 1000 meters?
A toy rocket is launched with an initial velocity of 180 m/s and its height is modeled by h = -5t² + 180t, where t is the time in seconds. How long will the rocket stay above a height of 1000 meters?
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A farmer has $5200 to spend on fencing for a pen along a river. The company charges $6.50 per meter for fencing. The farmer can choose between a rectangular pen with the river as one side or a right triangular pen with the hypotenuse along the river. Which shape maximizes the area of the pen?
A farmer has $5200 to spend on fencing for a pen along a river. The company charges $6.50 per meter for fencing. The farmer can choose between a rectangular pen with the river as one side or a right triangular pen with the hypotenuse along the river. Which shape maximizes the area of the pen?
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The cost per book (C) when a school orders yearbooks is modeled by C = 0.00005n² - 0.095n + 66.125, where n is the number of books ordered. What is the least cost per book, and how many yearbooks should be ordered to achieve this cost?
The cost per book (C) when a school orders yearbooks is modeled by C = 0.00005n² - 0.095n + 66.125, where n is the number of books ordered. What is the least cost per book, and how many yearbooks should be ordered to achieve this cost?
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A ball is thrown into the air, and its height (h) in meters after t seconds is modeled by h = -5t² + 20t + 1. After how many seconds, rounded to two decimal places, does the ball hit the ground?
A ball is thrown into the air, and its height (h) in meters after t seconds is modeled by h = -5t² + 20t + 1. After how many seconds, rounded to two decimal places, does the ball hit the ground?
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An object is thrown upward with an initial velocity of v m/s from an initial height of c meters. The height (h) after t seconds is modeled by h = -5t² + vt + c. What is the initial velocity of the object if it reaches its maximum height after 4 seconds?
An object is thrown upward with an initial velocity of v m/s from an initial height of c meters. The height (h) after t seconds is modeled by h = -5t² + vt + c. What is the initial velocity of the object if it reaches its maximum height after 4 seconds?
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The distance (d) a car travels while skidding is modeled by d = 250 + 50t - 4t², where t is the time in seconds taken to stop. How long does it take the car to stop?
The distance (d) a car travels while skidding is modeled by d = 250 + 50t - 4t², where t is the time in seconds taken to stop. How long does it take the car to stop?
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The city bus company carries an average of 3500 passengers daily, with each passenger paying $2.25. If the company increases the price by $0.25, the number of passengers decreases by 100. What is the fare that will maximize the company's revenue?
The city bus company carries an average of 3500 passengers daily, with each passenger paying $2.25. If the company increases the price by $0.25, the number of passengers decreases by 100. What is the fare that will maximize the company's revenue?
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What is the maximum daily revenue from coffee sales at The Next Cup coffee shop when the price per mug is optimized?
What is the maximum daily revenue from coffee sales at The Next Cup coffee shop when the price per mug is optimized?
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What was the height of the football at the moment it was kicked?
What was the height of the football at the moment it was kicked?
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For the parabola defined by y = -2(x + 5)² - 4, what is the value of the minimum?
For the parabola defined by y = -2(x + 5)² - 4, what is the value of the minimum?
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How many x-intercepts does the parabola y = -3x² have?
How many x-intercepts does the parabola y = -3x² have?
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What is the vertex of the parabola represented by y = 3x² + 18x + 21?
What is the vertex of the parabola represented by y = 3x² + 18x + 21?
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How long does it take for Baz Ketball's shot to reach its peak height?
How long does it take for Baz Ketball's shot to reach its peak height?
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In the function h = -5t² + 10t + 3, what is the distance above the floor when the ball reaches its peak?
In the function h = -5t² + 10t + 3, what is the distance above the floor when the ball reaches its peak?
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What is the equation of the parabola that has a vertex at (2,4) and a y-intercept of -4?
What is the equation of the parabola that has a vertex at (2,4) and a y-intercept of -4?
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What is the maximum revenue formula for a bus company in terms of price increases, given they lose customers?
What is the maximum revenue formula for a bus company in terms of price increases, given they lose customers?
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What dimensions will maximize the area for a garden that uses 24 m of fencing on three sides?
What dimensions will maximize the area for a garden that uses 24 m of fencing on three sides?
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To maximize sales revenue, at what price should Tom sell his T-shirts if he currently sells them at $10?
To maximize sales revenue, at what price should Tom sell his T-shirts if he currently sells them at $10?
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At what price should Mila set her CDs, originally priced at $20 with a drop in sales for every increase?
At what price should Mila set her CDs, originally priced at $20 with a drop in sales for every increase?
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How long will it take for the ball to reach a height of 35 m, given the height equation h = -4.9t^2 + 30t + 1.6?
How long will it take for the ball to reach a height of 35 m, given the height equation h = -4.9t^2 + 30t + 1.6?
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When will a ball thrown into the air hit the ground if described by h = -4.9(t - 2)^2 + 20?
When will a ball thrown into the air hit the ground if described by h = -4.9(t - 2)^2 + 20?
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What is the height equation for a wrench tossed on the moon?
What is the height equation for a wrench tossed on the moon?
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After how many seconds will the wrench hit the ground according to its height equation?
After how many seconds will the wrench hit the ground according to its height equation?
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Study Notes
Quadratic Relations
- Quadratic relations are relationships between variables that can be represented by a second-degree polynomial.
- The general form of a quadratic relation is y = ax² + bx + c, where 'a', 'b', and 'c' are constants.
- A quadratic relation has a graph that is a parabola.
- A parabola can open upwards or downwards depending on the value of 'a'.
- If 'a' is positive, the parabola opens upward.
- If 'a' is negative, the parabola opens downward.
- The vertex is the highest or lowest point on the parabola.
- The axis of symmetry is a vertical line that divides the parabola into two symmetrical halves.
- The zeros of a quadratic relation are the x-intercepts (the points where the graph crosses the x-axis).
- The y-intercept is the point where the graph crosses the y-axis.
- The domain of a quadratic relation is the set of all possible x-values.
- The range of a quadratic relation is the set of all possible y-values.
Transformations of Quadratics
- Transformations of quadratic functions involve shifting, stretching, compressing, or reflecting the graph of the basic quadratic function (y = x²).
- The vertex form of a quadratic function is y = a(x - h)² + k, where (h, k) represents the coordinates of the vertex.
- The value of 'a' affects the vertical stretch or compression of the parabola.
- A positive value of 'a' indicates an upward opening parabola.
- A negative value of 'a' indicates a downward opening parabola.
- The value of 'h' affects the horizontal translation of the parabola.
- A positive value of 'h' shifts the graph to the right.
- A negative value of 'h' shifts the graph to the left.
- The value of 'k' affects the vertical translation of the parabola.
- A positive value of 'k' shifts the graph upward.
- A negative value of 'k' shifts the graph downward.
Applications of Quadratics
- Quadratic functions can model various real-world situations, including projectile motion, optimization problems, and business scenarios.
- A range of word problems can be solved using quadratic relations such as profit maximization, projectile motion, or area maximisation
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Description
This quiz explores the concepts of quadratic relations, including their standard form, properties, and transformations. Learn about parabolas, their vertices, symmetry, and intercepts while deepening your understanding of these key mathematical principles.
