Vocabulary
The graph of a quadratic function
What is a parabola
Given the equation h(t)=-16t2+45t+5,
time is in seconds and height is in feet.
Name the Initial velocity AND Initial height.
Initial velocity- 45 ft/s
Initial height- 5 ft
What is the vertex and axis of symmetry of y=-3(x-2)2+1?
The axis of symmetry is 2 and the vertex is (2,1)
What is the axis of symmetry formula?
x = -b/(2a)
The affect the value of "a" has on the graph of the function f(x)=6.25x2 -2x + 3
What is narrower (steeper or vertically stretched) than the parent function, y = x2.
A function of the form y=ax2+bx+c
What is a standard form?
Given h(t)=-16t2+120t +50, name the axis of symmetry,
t = 3.75
What is the vertex and axis of symmetry of y=6(x+4)2+7?
The axis of symmetry is -4 and the vertex is (-4,7)
What information does c provide about the graph of f(x)=ax2+bx+c?
The value c corresponds to the y-intercept of the graph of f(x)=ax2+bx+c
The affect the value of A has on the graph of the function h(x)=-0.15x2
What is wider than the parent function and faces downward
The line that intersects the vertex and divides the graph into two congruent halves that are reflections of each other
What is the axis of symmetry?
What equation of a parabola will with contain the vertex (6, 7) and the point (8, 5)?
y = -0.5(x - 6)2 + 7
A diver jumps off a diving board into a pool. The height of the diver above the water can be modeled by the equation h(t)=-9.8t2+7t+3. What is the vertex and what is the maximum height the diver reaches?
Vertex (5/14, 4.25) or about (0.357, 4.25)
The maximum height is 4.25 meters
What is the axis of symmetry, vertex, and y-intercept of f(x)=2x2+4x+3?
Axis of Symmetry: x= -1
Vertex= (-1, 1)
Y-intercept= (0,3)
The affect the value of A has on the graph of the function h(x)=-9.25x2
What is narrower than the parent function and faces downward
The function f(x)+a(x-h)2+k
What is Vertex Form.
What is the y-intercept, domain and range for
y = 2(x - 3)2 - 10
y-intercept is (0, 8)
domain is all real numbers
range is y > -10
A company's main source of income is selling socks. The company's annual profit as a function of the price per pair of socks is modeled by: P(x)=-3(x-5)2+12. This is the sock price the company should set to earn a maximum profit. And what would the maximum profit be?
This means if the company sets the price of the socks to $5 they will earn a maximum profit which is $12 million
How is the standard form of a quadratic function different from the vertex form?
The standard form of a quadratic function tells you the y-intercept, while vertex for of a quadratic function tells you the vertex.
The graph of f(x)=ax2 opens downward and is narrower than the graph of the quadratic parent function. Which of the following could be the value of A?
A: -2 B: -0.5
C: 0.5 C: 1
What is A
How do you find the axis of symmetry from intercept form? Give the correct formula and meaning of it.
Average the x-intercepts
x = (p + q)/2
A diver jumps off a 20-ft high platform at an initial velocity of 8 ft/s. Find the diver's maximum height above the water. Use h(t)=-16t2+v0t +h0, where height is in feet and time is in seconds.
The diver's maximum height is 21 ft
The height (in meters) of the ball thrown into the air is given by the function h(t)=-4.9(t - 1.5)2+20, where t is the time in seconds.
How long does it take to reach its maximum height?
What is the maximum height reached by the ball?
It takes 1.5 seconds to reach its maximum height of 20 meters.
A football player kicked a 41-yard punt. The path of the ball was modeled by y = -0.035x2 + 1.4x +1, where x and y are measured in yards. The player kicked the football toward midfield from the 23 yard line. Over which yard line was the ball when it was at its maximum height? What is its maximum height
At the 43 yard line it reaches a maximum height of 15 yards.
A company is designing the trajectory of a new rocket launch. The height of the rocket, in meters, can be modeled by the quadratic function h(t)=-4.9t2+98t, where t represents the time, in seconds, since launch. What is the maximum reached by the rocket?
The maximum height reached by the rocket is 493 meters