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Category: Course Activities (Page 1 of 8)
The exam will cover the topics of Circles, Parabolas and Lines
Remember that the circle is defined by its CENTER and RADIUS
Remember that the important characteristics of a Parabola are: VERTEX, LINE OF SYMMETRY, X-Intercepts (“Roots”) and Y-Intercept
The Parabola has the two forms
General Form: $latex Ax^{2}+Bx+C=0$
Standard Form $latex A(x-h)^{2}+k=0$
The x-coordinate of the vertex is $latex \frac{-B}{2A}$
To get the y-coordinate of the vertex, put the x-value into $latex Ax^{2}+Bx+C$
and evaluate it.
The circle has the two forms
General Form: $latex Ax^{2}+Ay^{2}+Cx+Dy+C=0$
Standard Form $latex (x-h)^{2}+(y-k)^{2}=r^{2}$
The Center is at the point (h,k) and the radius = r.
Review these for the exam:
WebWork
Graphs-Graphs of Quadratic Equations. (Problems 1-4)
Graphs-Intro to Conics (Problems 1 and 12)
ShiftingParabolas (Understand all of these)
Graphs-Equation of a Line (Problems 4 and 6)
REMEMBER the 6-point process.
Here are practice problems for the exam:
Zero Product Rule
Solve $latex (x-2) (3x-7)=0$
Radical Equations
Solve $latex \sqrt{7s-3} +2 = 0$
Quadratic Equations
$latex \frac{1}{2}x^{2}+4=24$
$latex 2x^{2}+9x-5=0$
Rational Equations
$latex \frac{x}{x+6}=\frac{4}{7}$
$latex 1-\frac {5}{y}=-\frac{6}{y^{2}}$
Roots
Give a polynomial of degree 4 with roots 2,3,−1 and 0. You can keep it in factored form.
6-point process:
Apply the 6-point discussion to any of the above problems.
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