1. Day 2: Properties of Quadratics
Unit 4: Algebra of Quadratics

2. Learning Goals
To be able to describe and locate the properties of a quadratic

3. Draw the graph 𝑦= 𝑥 2 𝑥 𝑦 −3 −2 −1 1 2 3 9 4 1

4. Domain
What are the possible values of 𝑥?

5. Range
What are the possible values of 𝑦?

6. Axis of Symmetry
What value of 𝑥 cuts the graph
evenly?

7. Vertex
What coordinates are the turn
around point?

8. Maximum or Minimum? Is there a maximum or a minimum 𝑦 value?
What would the graph look like if it
had a maximum?

9. Optimal Value
What is the 𝑦 value of that
maximum or minimum?

10. Direction of Opening
Is the parabola facing up or down?

11. Zeroes At which 𝑥 value(s) does the graph touch/cross the 𝑥-axis? or
What are the possible values for 𝑥
that make 𝑦=0?

12. Zeroes At which 𝑥 value(s) does the graph touch/cross the 𝑥-axis? or
What are the possible values for 𝑥
that make 𝑦=0?

13. Zeroes At which 𝑥 value(s) does the graph touch/cross the 𝑥-axis? or
What are the possible values for 𝑥
that make 𝑦=0?

14. Determine the zeroes of each quadratic equation.
b) 𝐴=2𝑤(18−𝑤)

15. Each pair of coordinates is located on the opposite side of the same parabola. Determine the equation of the axis of symmetry.
a) 3, 2 & (9, 2)
b) −4.5, 5 & (−1.5, 5)

16. The zeroes of a quadratic relation are 2 and −6, and the second differences are positive. What is the value of 𝑥 that produces the optimal value?

17. To find the zeroes:
Let 𝑦=0 and solve for 𝑥 (0, 1 or 2 possibilities)
To find the axis of symmetry:
Find the average of the 𝑥 coordinates with the same 𝑦 value

18. Second differences:
If positive, graph opens up
If negative, graph opens down
Optimal value:
Occurs on the axis of symmetry

19. Success Criteria
I CAN locate and describe the properties of a quadratic including:
Domain
Range
Axis of symmetry
Vertex
Maximum or minimum
Optimal value
Direction of opening
Zeroes (𝑥-intercepts/roots)

20. To Do…
Worksheet
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