Day 2: Properties of Quadratics

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Presentation transcript:

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

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

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

Domain What are the possible values of 𝑥?

Range What are the possible values of 𝑦?

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

Vertex What coordinates are the turn around point?

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

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

Direction of Opening Is the parabola facing up or down?

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?

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?

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?

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

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)

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?

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

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

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)

To Do… Worksheet Check the website daily for updates, missed notes, assignment solutions www.mrsmccrum.weebly.com New: note outline available the night before (completed note will no longer be posted)