Patterns & Growth
This type of pattern features output values that do not change by equal amounts or equal factors, but instead often increase and then decrease.
What is a quadratic pattern?
For a rectangular garden with a fixed perimeter of 50 meters, this side length (in meters) will result in the largest possible area.
What is 12.5 meters?
This is the specific name for the highest or lowest point on a parabola.
What is the vertex?
This form of a quadratic expression is written as ax2+bx+c.
What is standard form?
In the projectile motion equation h(t)= 5 + 60t − 16t2, this constant term indicates how many feet the object was above the ground when launched.
What is 5 feet?
This type of growth eventually results in the largest output values for sufficiently large inputs, even if it starts off growing more slowly than quadratic growth.
What is exponential growth?
This specific type of rectangle has four equal side lengths and is often the solution for maximizing area within a fixed perimeter.
What is a square?
These are the input values of a function that result in an output value of exactly zero.
What are the zeros (or horizontal intercepts)?
This form of a quadratic expression is written as a product of two linear factors, such as (x+p)(x+q).
What is factored form?
In the projectile motion equation h(t)= 5 + 60t − 16t2, this specific term in a height equation accounts for the downward pull of the Earth on a projectile
What is −16t2?
This visual feature describes the "U" shape of a quadratic function's graph.
What is a parabola?
If a rectangle has a fixed perimeter of 40inches, the relationship between its length (l) and width (w) is defined by this linear equation.
What is l+w=20 (or w=20−l)?
This point on a graph represents the initial height of a launched object at the moment t=0.
What is the vertical intercept (or y-intercept)?
his form, y=a(x−h)2+k, is named for its ability to clearly show the coordinates (h,k) of the graph's most important point.
What is vertex form?
In a business context, this value is found by multiplying the price of a product by the number of sales or downloads predicted at that price.
What is revenue?
In a dot pattern where Step n is represented by an n-by-n square, the expression for the total number of dots is n2
What is a quadratic relationship?
In a geometric pattern where Step n is an n-by-n square with one extra square on top, this expression represents the total number of squares.
What is n2+1?
If the vertex of a parabola is the highest point on the graph, the parabola is said to open in this direction.
What is downward?
This mathematical property is used to expand factored expressions like (x+2)(x+3) into their standard form equivalent.
What is the distributive property?
This term refers to the set of all possible input values that are meaningful or appropriate for a given real-world situation.
What is the domain?
Unlike quadratic growth, this type of growth features a constant rate of change where the same amount is added for each equal interval.
What is linear growth?
In the equation d=16t2, this is what the variable d represents for a falling object after t seconds.
What is the distance fallen?
On a quadratic graph, the x-coordinate of the vertex is always located at this relative position between the two x-intercepts.
What is the halfway point?
When a quadratic expression has a negative coefficient for its squared term, the graph will always exhibit this behavior.
What is opening downward?
When a function models a jumping frog or a catapulted pumpkin, this is the height at the moment it lands back on the ground.
What is zero or horizontal intercept?