Solutions
Solve. x2+3x-28=0
x={-7,4}
A soccer player kicks the ball! The function f(x)=-16x2+64x represents the height of the soccer ball in feet after x seconds. What is the domain of the function?
[0,4]
Which function has a larger minimum?
f(x)=2x2-12x+9 or k(x)=2(x-1)2-8
k(x)
Convert to VERTEX form.
f(x)=x2-18x+70
y=(x-9)2-11
Marty is practicing his tennis swing. He is hitting tennis balls over the net. The function f(x)=-1/8x2+x+3 models him hitting a tennis ball. What is an appropriate domain for this situation? Round any decimals to the nearest hundredth.
[0,10.32]
Solve. 5x2-15x=0
x={0,3}
A soccer player kicks the ball! The function f(x)=-16x2+64x represents the height of the soccer ball in feet after x seconds. What is the range of the function?
[0,64]
Which function has a larger y-intercept?
g(x)=2x+4 or m(x)=2(x-1)2-8
g(x)
Convert to VERTEX form.
y=(x+7)2-14
Marty is practicing his tennis swing. He is hitting tennis balls over the net. The function f(x)=-1/8x2+x+3 models him hitting a tennis ball. What is an appropriate range for this situation? Round any decimals to the nearest hundredth.
[0,5]
x={-7/4,7/4}
A student is tossing a pickleball from the top of the gym to the bottom. The function f(x)=-16x2+x+24 models the pickleball in feet after x seconds. What is the domain and range for this function?
Domain: [0,1.25]
Range: [0,24]
Mary Beth is launching a rocket in the sky at this year's science fair! Her rocket is supposed to break the record to the highest launch at her school. She is super stoked to watch it happen!
Which function would model this situation?a) f(x)=4x-8
b) g(x)=x2-10x-12
c) h(x)=-6x2+50x+2
c) h(x)=-6x2+50x+2
Choice a shows the rocket staying in the sky forever and choice b shows the rocket going underground/ underwater and then resurfacing.
Convert to STANDARD form.
y=3(x+4)2-10
y=3x2+24x+38
Penelope is working on her egg drop project. She has to drop an egg from the top of a building without it breaking. Her drop is modeled by h(t)=-3t2+12. What is the domain of this function?
[0,2]
Factor to find the x-intercepts of the function f(x)=2x2-3x-20.
(-5/2,0) (4,0)
A swimmer is diving into the pool! What interval below could represent the DOMAIN of this scenario?
a) [-3, -7]
b) [0,8]
c) [-4,0]
b) [0,8]
Domain refers to time which will ALWAYS be positive!
Write an equation for a parabola that has a y-intercept greater than the function below.
f(x)=5x2-9x+4
Answers Vary. Mrs. Herold will check your work! Your y-intercept needs to be a value greater than 4!
Convert to FACTORED form.
f(x)=-6x2+36x-30
y=-6(x-5)(x-1)
Penelope is working on her egg drop project. She has to drop an egg from the top of a building without it breaking. Her drop is modeled by h(t)=-3t2+12. If I told you the range was [0,2], would you agree or disagree? WHY?
Disagree. The range is [0,12], because the minimum height is 0 and the maximum height is 12. [0,2] represents the domain which is time.
What are the solutions to the function y=x2-10x+12? Round your decimals to the nearest hundredths.
x={1.39,8.61}
A swimmer is diving into the pool! What interval below could represent the RANGE of this scenario?
a) [4,0]
b) [-6,28]
c) [-5,0]
d) [0,7]
c) [-5,0]
The swimmer would be going underwater which allows for negative height. He jumped in at 0 feet and went down 5 feet before coming back up to 0.
Write an equation for a parabola that has a minimum less than the function below.
g(x)=2(x-3)2-9
Answers Vary! Mrs. Herold will check your answer. Your vertex should have a k value that is less than -9.
What form of quadratic functions tells me transformations, axis of symmetry, and direction of opening?
VERTEX FORM
In CONTEXT, what does domain refer to? What does range refer to?
domain refers to time
range refers to height