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All Things Vertex
Name the Function Type
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100
What is the definition of the vertex of a function?
The lowest, or highest point of the graph depending on if the graph is opening upward or downward.
100
What type of function has a common ratio among the y-values while the x-values grow by a constant rate?
Exponential
100
What is the parent function for a quadratic function?
f(x)= x²
200
What is the vertex of the following equation written in vertex form? f(x)= 8(x+5) - 7
(-5,-7)
200
What type of function could represent a table that has x-values that are growing by a constant number and y-values that have a first common difference?
Linear
200
f(x) = a(x-h)²+k is what?
Vertex form of a quadratic equation
300
What is the vertex for the equation f(x)= 3x²+6x+8? Show by completing the square.
(-1,5)
300
Paul is presented with a graph that is u-shaped and has an axis of symmetry, two x-intercepts, and one y-intercept. What type of function is Paul presented with?
Quadratic
300
Complete the square for the following equation: g(x)= x² + 10x - 7
(x+5)² - 32
400
Find the vertex for the following function by completing the square. f(x)= 30x² - 60x + 8
(1,-22)
400
A rock is thrown from the top of a tall building. It travels at an initial velocity of 20 feet per second. The height of the building is 30 feet. What type of function can be used to model how long it would take for the rock to hit the ground? (Bonus 100 Points: Write an equation to model the relationship between the height of the rock, h, and time in t seconds)
Quadratic h(t)= -16t² + 20t + 30
400
Kelly looks at the graph of a quadratic function. She sees the graph is opening downward and crosses the y-axis at (0,8). Which of the following can be a possible equation for the graph she is looking at? a) f(x)= 2x² + 8 or b) f(x)= -2x² + 8 or c) f(x)= 2x² - 8 or d) f(x)= -2x² - 8
b) f(x)= -2x² + 8
500
Write an equation in vertex form using the following information: Vertex: (3,1) Two additional points on the graph: (4,4) (2,4)
f(x)=3(x-3)²+1
500
There is a population of 1,000,000 bacteria in a colony. The number of bacteria doubles every 30 minutes. What type of function could be used to model the number of bacteria present after t hours? What is the equation that would be used to model this problem.
Exponential f(t)= 1,000,000(2)^2t
500
What are the zeros of the following quadratic function? h(x) = 4x² +28x + 48
-3 and -4