Graphs of Quadratics
Find the vertex of:
y = x2 + 8x + 15
(-4, -1)
Solve by graphing. Round to the nearest tenth if necessary.
y = 3x2 + x - 7
x = -1.7
x = 1.36
Solve using the Quadratic Formula
4x2 = 8x + 60
x = 5
x = -3
Find the discriminant and tell the number of solutions.
x2 + 3x + 20 = 0
Discriminant = -72
Number of Solutions: None
McDonalds sells Big Macs for $3 each. At this price, they sell an average of 103 Big Macs per day. Based on customer feedback, the store manager predicts that he would sell 15 more Big Macs per day for each $0.50 decrease in price.
Write a function P(x) to represent the price of the Big Macs.
Write a function T(x) to represent the number of Big Macs sold per day.
P(x) = 3 - 0.50x
T(x) = 103 + 15x
Find the axis of symmetry of:
y = x2 + 8x + 15
x = -4
Solve using factoring and the zero product property.
t2 - 9t + 18 = 0
x = 3
x = 6
Solve by Complete the Square
x2 + 6x = 7
x = 1
x = -7
Identify whether the function is linear, exponential, or quadratic. Then WRITE AN EQUATION for the function.
x| -2, -1, 0, 1, 2
y| 3, 2, 3, 6, 11
Quadratic; y = x2 + 2x + 3
McDonalds sells Big Macs for $3 each. At this price, they sell an average of 103 Big Macs per day. Based on customer feedback, the store manager predicts that he would sell 15 more Big Macs per day for each $0.50 decrease in price.
Let P(x) = 3 - 0.50x
Let T(x) = 103 + 15x
Find R(x) representing the revenue from sales.
R(x) = -7.5x2 - 6.5x + 309
Find the domain and range of:
y = x2 + 8x + 15
Domain: All real numbers
Range: y >= -1
Solve using factoring and the zero product property.
28g - 7g2 = 0
g = 0
g = 4
Solve using the Quadratic Formula
5x2 + 15x + 16 = 0
No solution
Given f(x) = x2 + 8x - 9, g(x) x - 5 and h(x) = x + 4,
Find (f+g)(x)
x2 + 9x - 5
If a toy rocket is launched vertically upward from ground level with aninitial velocity of 10 feet per second, then its height y after t seconds is given by the equation y = -16t2 + 30t
a) How long will it take for the rocket to return to the ground?
b) How long will it take the rocket to hit its maximum height?
a) ~1.875sec
b) ~0.937 sec
Find the y-intercept of:
y = 2x2 + 3x + 10
(0, 10)
Find the zeros by graphing.
y = x2 + 8x + 15
x = -5
x = -3
Solve using the Quadratic Formula
3x2 + 6x = 10
-3 +- sqrt(39)
____________
3
Identify whether the function is linear, exponential, or quadratic. Then WRITE AN EQUATION for the function.
x| -3, -2, -1, 0, 1, 2
y| 5/64, 5/16, 5/4, 5, 20, 80
Exponential; y = 5(4)x
If a toy rocket is launched vertically upward from ground level with aninitial velocity of 10 feet per second, then its height y after t seconds is given by the equation y = -16t2 + 30t
c) What is the maximum height?
d) How high off the ground will the rocket be after 1 second? Does this value make sense?
c) ~14.06ft
d) 14ft; yes! It seems reasonable that a rocket could be 14ft off the ground if shot quickly upward in 1 second.
Find the max/min value of of:
y = x2 + 8x + 15
y = -1
Solve using factoring and the zero product property.
30h - 45h2 = 0
h = 0
h = 2/3
Solve using Complete the Square
3x2 - 24x + 30 = 0
x = 4 +- sqrt(6)
Find (f*g)(x)
x3 + 3x2 - 49x + 45
Write an equation in vertex form given the vertex and a point. Then convert to standard form.
V(4, -5) P(2, 7)
Vertex Form: y = 3(x-4)2 - 5
Standard Form: 3x2 - 24x + 43