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Nuffield Free-Standing Mathematics Activity Completing the square

Nuffield Free-Standing Mathematics Activity Completing the square. Example. Application. To find the maximum or minimum value of this function. Minimum value of . Completing the square. means writing the unknown terms of a quadratic in a square bracket. because.

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Nuffield Free-Standing Mathematics Activity Completing the square

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  1. Nuffield Free-Standing Mathematics Activity Completing the square

  2. Example Application To find the maximum or minimum value of this function. Minimum value of Completing the square means writing the unknown terms of a quadratic in a square bracket because Think about…What is always true about the value of (x + 3)2?What will always be true for (x + 3)2 – 2? is–2

  3. Application To find the minimum point on the graph of the function. Think about… For what value of x is (x + 3)2 – 2 a minimum? has a minimum value when x = –3 Minimum point on the curve is(–3 , –2) Think about… What shape is the graph of y = x2 + 6x + 7 ? Can completing the square help you sketch the graph of a quadratic?

  4. y 7 x 0 Graph of y = x2 + 6x + 7 line of symmetry x = –3 Minimum point is(–3 , –2) x = –3 is a line of symmetry When x= 0, y = 7 (–3, –2) So the intercept on the y axis is 7

  5. To sketch the graph of line of symmetry y 5 (1, 3) x 0 Example Think about…What is the maximum or minimum value? Think about…What shape will the graph be? Where is its turning point? has a minimum value when x = 1 Minimum point is(1, 3) Intercept on the y axis is5 x = 1

  6. To sketch the graphof y (–2, 7) 3 x 0 x = –2 Example Think about…What is the maximum or minimum value? Think about… What shape will the graph be? Where is its turning point? has a maximum value when x = –2 Maximum point is(–2, 7) Intercept on the y axis is3 Note you can find the intercepts on the x axis by solving

  7. Completing the square Reflect on your work How does completing the square help you to sketch the graph of the function? Can you use completing the square to tell you whether the quadratic function has any real roots?

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