6 Questions
Projectile motion involves the study of objects in ______
motion
To find the vertex of a quadratic equation, one method is by completing the ______
square
Factoring and applying the zero-product property is a method to solve quadratic equations and find ______
x-intercepts
In standard form of a quadratic function, the equation is y = ax^2 + bx + ______
c
The factored form of a quadratic function is y = a(x - r)(x - s), where r and s are the ______
x-intercepts
Determining the domain and range for quadratic functions helps define their ______
notation
Study Notes
Quadratic Applications
- Projectile motion and Bridge arch problems can be modeled using quadratic equations
- Finding Maxima and Minima: e.g., Max area, height, etc. using quadratic equations
Revenue and Profit
- Revenue = Price × Quantity
- Profit = Revenue – Expenses = (# sold)(price) – (#sold)(cost price)
- Vertex represents maximum revenue or profit
Finding the Vertex of a Quadratic
- Completing the square to find the vertex
- Calculating the midpoint of the x-intercepts and then substituting back into equation to find y
- Using the formula x = -b / 2a to calculate the x-coordinate of the vertex (axis of symmetry) and then substituting back into equation to find y
- Vertex represents the highest/lowest point (max if a < 0 /min if a > 0)
Solving Quadratic Equations
- Factoring and applying the zero-product property to find x-intercepts
- Using the quadratic formula: x = (-b ± √(b² - 4ac)) / 2a to find x-intercepts
- X-intercepts represent where the object hits the ground (or similar)
Converting between Quadratic Forms
- Converting between standard form, vertex form, and factored form
- Refer to Flowchart on Page 3 for summary
Graphing Quadratic Functions
- Graphing quadratic functions in standard form: y = ax² + bx + c
- Graphing quadratic functions in vertex form: y = a(x – h)² + k, where (h, k) = vertex
- Graphing quadratic functions in factored form: y = a(x – r)(x – s), where r, s are the x-intercepts
- Key points to label: y-intercept, x-intercepts, vertex
Domain and Range
- Determining the Domain and Range for quadratic functions using proper notation
This quiz covers word problems involving quadratic equations such as projectile motion and bridge arch problems, as well as finding maxima and minima (e.g., max area, height) by determining the vertex. Learn how to find the vertex of a quadratic equation using methods like completing the square and calculating the midpoint of x-intercepts.
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