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2.1.2 notes
OCT 13 and OCT 17
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WARMUP: (do on back of notes or
separate sheet)
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Summarize the mathematics
a)
In general, to solve the inequality f(x) ≤ c, look for points
on the graph of f(x) lying on or below the line y = c. To
solve f(x) ≥ c, look for points on or above that horizontal
line. Then identify the x values associated with those
points.
b)
c)
x ≤ -2 or x > 4
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QUADRATIC INEQUALITIES
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What is a quadratic function?
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Standard form?
In standard form, how can we determine:
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x – intercepts?
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y – intercepts?
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How do we know if a quadratic opens up or opens down?
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How do we solve quadratic functions?
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2.1.2 problems
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Problems 1 – 6
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Homework:
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Finish problems 1 – 6 if not finished already
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Check your understanding worksheet
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Quiz next class on 2.1.1 and 2.1.2
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2.1.2 SUMMARY
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2.1.2 SUMMARY
a)
One effective strategy for solving inequalities in the form ax2
+ bx + c ≤ d and ax2 + bx + c ≥ d would be to rewrite the
inequality in less than or equal to 0 or greater than or equal to
0 to identify values of x (x-intercepts) that bound the solution
intervals for the inequalities, and use cues from the graph to
decide which interval(s) satisfy each inequality. The x – values
at which the graph is at or below the x-axis will be solutions of
the ≤ inequality. The x – values at which the graph is at or
above the x –axis will be solutions of the ≥ inequality. This
strategy also applies when d = 0
b)
Solutions for a quadratic inequality may be of the form “x≤m
or x≥n” or “m≤x≤n”. The corresponding number line graphs
will look like these:
c)
It is possible to have no real solutions or a solution of one
value, as seen in problem 5. Also, if the inequality is a strict
inequality, the number lines above would have dots on m and
n