3.3 Connecting Intercepts, zeros and Solutions (11/19/24)
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Last updated 12 months ago
22 questions
Essential Question:How can you use the graph of a quadratic function to solve its related quadratic equation?
Learning Target: Students will be able graph a quadratic function, and use the graph to find its y-intercepts and explain the significance of the points.
Show you work and use complete sentences for credit.
Day 1 11/18/24
Required
5 points
5
Question 1
1.
What is the value of x for every point on the axis of symmetry?
Required
5 points
5
Question 2
2.
What are the coordinates of the vertex?
Required
5 points
5
Question 3
3.
The vertex will always be on the_____________
Required
5 points
5
Question 4
4.
How many zeros does this parabola have?
Required
10 points
10
Question 5
5.
What are the x-values of the zeroes?
Left zero [Your answer should be in the coordinate form (x,y) ]
_______
Right zero [Your answer should be in the coordinate form (x,y) ]
_______
Required
5 points
5
Question 6
6.
The y-value of the zeroes is always______________
Required
10 points
10
Question 7
7.
What are two other names that mean the same as the "zeroes of the quadratic equation" ? (If you do not know do a quick search on Google.)
_______
_______
Required
40 points
40
Question 8
8.
Use the graph to find the features of this quadratic equation.
What is the axis of symmetry? (Use the form x=__ for your answer.
_______
What is the vertex? [Your answer should be in the coordinate form (x,y) ]
_______
What is one zero of the equation? (Write your answer in the form x=___)
_______
What is another zero of the equation?(Write your answer in the form x=___)
_______
Required
40 points
40
Question 9
9.
Use the graph to find the features of this quadratic equation.
What is the axis of symmetry? (Use the form x=__ for your answer.
_______
What is the vertex? [Your answer should be in the coordinate form (x,y) ]
_______
What is one zero of the equation? (Write your answer in the form x=___)
_______
What is another zero of the equation?(Write your answer in the form x=___)
_______
Required
40 points
40
Question 10
10.
Use the graph to find the features of this quadratic equation.
What is the axis of symmetry? (Use the form x=__ for your answer.
_______
What is the vertex? [Your answer should be in the coordinate form (x,y) ]
_______
What is one zero of the equation? (Write your answer in the form x=___)
_______
What is another zero of the equation?(Write your answer in the form x=___)
_______
Required
40 points
40
Question 11
11.
Use the graph to find the features of this quadratic equation.
What is the axis of symmetry? (Use the form x=__ for your answer.
_______
What is the vertex? [Your answer should be in the coordinate form (x,y) ]
_______
What is one zero of the equation? (Write your answer in the form x=___)
_______
What is another zero of the equation?(Write your answer in the form x=___)
_______
Required
40 points
40
Question 12
12.
Use the graph to find the features of this quadratic equation.
What is the axis of symmetry? (Use the form x=__ for your answer.
_______
What is the vertex? [Your answer should be in the coordinate form (x,y) ]
_______
What is one zero of the equation? (Write your answer in the form x=___)
_______
What is another zero of the equation?(Write your answer in the form x=___)
_______
Required
40 points
40
Question 13
13.
Fill the table of values and graph the Quadratic Function.
What is the axis of symmetry? (Use the form x=__ for your answer.)_______
What is the vertex? [Your answer should be in the coordinate form (x,y) ]_______
What is one zero of the equation? (Write your answer in the form x=___)
_______
What is another zero of the equation?(Write your answer in the form x=___)
_______
Required
40 points
40
Question 14
14.
Fill the table of values and graph the Quadratic Function.
What is the axis of symmetry? (Use the form x=__ for your answer.)_______
What is the vertex?_______
What is one zero of the equation?(Write your answer in the form x=___)
_______
What is another zero of the equation?(Write your answer in the form x=___)
_______
Required
40 points
40
Question 15
15.
Fill the table of values and graph the Quadratic Function.
What is the axis of symmetry? (Use the form x=__ for your answer.)
_______
What is the vertex?
_______
What is one zero of the equation?(Write your answer in the form x=___)
_______
What is another zero of the equation?(Write your answer in the form x=___)
_______
Required
40 points
40
Question 16
16.
Fill the table of values and graph the Quadratic Function.
What is the axis of symmetry? (Use the form x=__ for your answer.)
_______
What is the vertex?
_______
What is one zero of the equation?(Write your answer in the form x=___)
_______
What is another zero of the equation?(Write your answer in the form x=___)
_______
Required
40 points
40
Question 17
17.
Fill the table of values and graph the Quadratic Function.
What is the axis of symmetry? (Use the form x=__ for your answer.)
_______
What is the vertex?
_______
What is one zero of the equation?(Write your answer in the form x=___)
_______
What is another zero of the equation?(Write your answer in the form x=___)
_______
Required
40 points
40
Question 18
18.
Fill the table of values and graph the Quadratic Function.
What is the axis of symmetry? (Use the form x=__ for your answer.)
_______
What is the vertex?
_______
What is one zero of the equation?(Write your answer in the form x=___)
_______
What is another zero of the equation?(Write your answer in the form x=___)
_______
For the next 4 problems, create a quadratic equation then solve the equation with a related function. You can use this graphing calculator to help you.
Required
10 points
10
Question 19
19.
A competitive diver stands at the end of a 30-foot platform and falls forward into a dive.
The function h(t) = −16t² + 30, where t represent the time in seconds, gives the height h, in feet, of the diver as he falls.
How long is the diver in the air? Round your answer to the nearest tenth of a second.
_______
When is he 20 feet in the air? Round your answer to the nearest tenth of a second.
_______
Required
10 points
10
Question 20
20.
Nature A bird is in a tree 60 feet off the ground and drops a twig that lands on a
rosebush 25 feet below. The function h (t) = -16t² + 60, where t represents the time
in seconds, gives the height h, in feet, of the twig above the ground as it falls.
When will the twig land on the bush? Round your answer to the nearest hundredth place.
_______
If the bush was not there, when would the twig hit the ground? Round your answer to the nearest hundredth place.
_______
Required
10 points
10
Question 21
21.
A basketball player named Orlando successfully makes a free throw. The height of the ball above the ground can be modeled by the quadratic function f(t) = −16t² + 27t + 6 where t is the time the ball is in the air. The basket is 10 feet above the ground.
How long does it take the ball to get to the basket? Round your answer to the nearest tenth of a second.
_______
If Orlando shoots an airball, how long would it take to hit the ground? Round your answer to the nearest tenth of a second.
_______
Required
10 points
10
Question 22
22.
A baseball coach uses a pitching machine to simulate pop flies during
practice. The quadratic function ƒ (x) = -16x² + 70x + 10 models the height in feet
of the baseball after x seconds.
How high does the ball get in the air? Round your answer to the nearest tenth of a second.
_______
How long is the baseball in the air if the ball is not
caught? Round your answer to the nearest tenths place.
