Quadratic Graphs
What is the domain of a quadratic function?
What is all real numbers?
The value of "a" for a graph of a quadratic function that is concave down.
What is negative?
The coordinates of the y-intercept for the quadratic function:
y=-2x2 + 5x - 7
What is (0,-7)?
A diver's motion when jumping off a diving board can be modeled by h(t) = -16t2 + 8t + 14. How high is the diving board?
14 feet above the water
Increasing and decreasing intervals are listed using what variable?
What is x?
The shape of the graph of a quadratic function.
What is a parabola?
Describe all transformations of p(x)= (x+8)2 - 6 from the parent function
shift left 8, shift down 6
The vertex of the quadratic equation:
y = x2 - 8x - 20
What is (-4,28)
If the equation h(t) = -16t2 + 18t + 5 models the height in feet of a ball above the ground after t seconds, what is the initial velocity?
What is 18 feet per second?
On what interval is y = x2 + 6x + 5 increasing?
What is x > -3?
The name of the line that divides a quadratic function exactly in half.
What is the axis of symmetry?
Write a function g(x) that represents the parent function after a reflection over the x-axis, a shift right 8 units, and a shift down 17 units
g(x) = -(x - 8)2 - 17
Find the vertex for the quadratic function:
y = x2 + 10x + 6
What is (-5, -19)
If the equation h(t) = -16t2 + 18t + 5 models the height in feet of a ball above the ground after t seconds, what is the maximum height, rounded to the nearest hundredth?
What is 10.06 feet?
What is the average ROC over the interval [2,3] for the function f(x) = 2x2 - 5
What is 10?
The vertex of the quadratic function y = 5x2 + 10x - 2 is a ______________ (maximium or minimum)?
What is minimum?
The graph of f(x) is shifted down 6 units. Which of the following key features remain the same?
domain, range, axis of symmetry, vertex
domain and the axis of symmetry
The coordinate for the positive x-intercept for this quadratic function, rounded to the nearest tenth:
y = x2 - 8x - 3
What is (8.4,0)?
If the equation h(t) = -16t2 + 16t + 7 models the height in feet of a ball above the ground after t seconds, when does the ball land on the ground, rounded to the nearest tenth?
What is 1.3 seconds?
What is the average ROC over the interval [-2,1] for the function modeled below?
x: -3 -2 -1 0 1 2 3
y: 76 54 36 22 12 6 4
What is -14?
How many zeros (x-intercepts) can a quadratic function have?
What is 2, 1, or none?
Suppose the function f(x) = 3x2 + kx + 67 is a translation down 8 units and left 5 units of the function g(x) = 3x2. What is the value of k?
What is k=30?
Which has a larger minimum, f(x) or g(x)?
f(x) = x2 - 4x + 8
g(x) = x2 - 2x + 6
What is g(x)?
An orange is thrown off a 60ft cliff at an initial velocity of 32 ft/sec. An apple is thrown from 6ft further downhill at an initial velocity that is 5 ft/sec faster than the apple. Which fruit goes higher?
What is the orange?
On what interval is the function f(x) = 1/2x2 + 5x + 8 decreasing?
x < -5