Quadratic Functions, Equations and Inequalities

Quadratic Functions, Equations and Inequalities

Secondary 3

Consider the function \(y=x^2-2x-3.\)

  1. Complete the table.

    \(x\)\(-2\)\(-1\)\(0\)\(1\)\(2\)\(3\)\(4\)
    \(y\)
  2. Draw the curve for \(-2\le x\le4\). Use a vertical range of \(-5\le y\le6\).

    On the same axes, draw the horizontal line \(y=2\).

  3. Use the intersections to solve\[ x^2-2x-5=0. \]

    Give your answers to 1 decimal place and explain why the line \(y=2\) is appropriate.

Solution:

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Answer:(a) \(y\)-values: \(5,0,-3,-4,-3,0,5\); (c) roots \(x\approx-1.4,\ 3.4\).

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