Vocabulary
Vertex
What is the point where a quadratic equation changes directions. The highest or lowest point in a parabola.
A streaming service charges a $10 monthly base fee plus $2 per movie rental. Write a function C(x) for the total cost of renting x movies in a month.
What is C(x) = 2x +10.
A ride-share app uses C(m) = 2.50m + 3.00 to calculate fare. What does the y-intercept represent in real life?
Evaluate f(x) = 4x - 7
for x = 5
What is 13
Solve for x:
3x - 9 = 0
What is 3.
Slope
What is the rate that a linear equation changes. Expressed as rise (vertical movement) over run(horizontal movement).
You start the week with $20 in your lunch account and add $5 each day. Write a function B(d) for your account balance after d days.
What is B(d) = 5d + 20.
A high diver's height above the water is modeled by h(t) = -16t2 + 16t + 32. What real-world information does the vertex give you?
What is the maximum height of the dive and the time it takes to reach that height.
Evaluate g(x) = x2 - 3x + 2
for x = -2
What is 12
Solve for x by factoring:
x2 - 16 = 0
What is x = 4 and x = -4.
Coefficient
What is the value that a variable is multiplied by in a function.
A water balloon thrown upward from a platform of 10 meters hits the ground after 2.5 seconds knowing that gravity is expressed in a quadratic function as-4.9 m/s2 write the equation for its height over time by finding its initial velocity.
What is h(s) = -4.9t2 + 8.25x + 10
You track your phone battery percentage using B(h) = -12.5h + 100. What does the x-intercept represent?
The time it takes for your battery to completely die.
For k(x) = (x2 + 3)/4 + 3
find k(5)
What is 10
Solve for x by factoring:
x2 - 7x + 12 = 0
What is x = 4 and x = 3
Domain
What is the set of all possible (used) x values. The input values that are relevant and possible in a function.
A skateboard deck drops in value by $15 per month. If it is worth $60 after 3 months, write a slope-intercept equation V(m) for its value after m months.
What is V(m) = -15m + 105.
A student club tracks revenue from selling t-shirts using R(x) = -5x2 + 150x, where x is the shirt price. At $30 the student club would make no money. What shirt price yields the maximum revenue?
What is $15.
If h(x) = -2(x + 1)2 + 8,
find h(3)
What is -24
Find the exact solutions to
x2 - 6x + 2 = 0
by factoring or using the quadratic formula
What is x = 3 + √ 7 and x = 3 - √ 7
Function
What is the mathematical relationship between an input and its output. For each input there exists one and only one possible output.
A basketball is thrown from a platform 7 feet above the ground. It reaches its maximum height of 16 feet at a horizontal distance of 6 feet. Write the quadratic function H(d) that models the ball's height above the ground based on distance thrown.
What is
H(d) = -.25d2 + 3d + 7.
A model rocket's flight path is given by h(t) = -16t2 + 96t. What does the positive t-intercept represent in this context?
What is the moment the rocket lands back on the ground.
For f(x) = 3x2 - 5x + 4, find
f(a + 1) in standard form.
What is 3a2 + a + 2
Find all solutions to
2(x - 4)2 - 32 = 0
What is x = 8 and x = 0.