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Chapter 9 Resource Masters
-8. -12. 8. -4. -8 f(x). 4 x. O f(x). 9-2 Study Guide and Intervention. Solving Quadratic Equations by Graphing. Example 1. Example 2
10-8 Study Guide and Intervention - Equations of Circles
9. 10. Standard Equation of a Circle. An equation for a circle with center at (h k).
10-8 - Study Guide and Intervention
Lesson 10-8. Chapter 10. 49. Glencoe Geometry. Study Guide and Intervention. Equations of Circles. Equation of a Circle A circle is the locus of points in a.
9-1 Study Guide and Intervention - Graphing Quadratic Functions
parabola opens upward and the vertex is a minimum point. d. Graph the function. Exercises. Consider each equation. Determine whether the function has a maximum
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4p=12. P = 3. 17. 8 12. Glencoe Precalculus. Page 2. NAME. DATE. PERIOD. 7-1 Study Guide and Intervention (continued). Parabolas. Equations of Parabolas
9-2 Study Guide and Intervention - Solving Quadratic Equations by
The vertex of the parabola is the x-intercept. Thus the only solution is 3. Exercises. Solve each equation by graphing. 1.
The Parabola and the Circle - San Antonio
+ Cx + Dy + E = 0 where A & B ? 0. Math 0303. Student Learning Assistance Center - San Antonio College. 7. Page 8. Example 4: Find the equation of a circle
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4-1 Study Guide and Intervention The equation of the axis of symmetry is x = ... 8. {f(x)f(x) ?9?} f(1)=3(1)² — 6(1) + 7 = 4 so the minimum value.
Study Guide and Intervention
Study Guide and Intervention. Solving Absolute Value Equations. Evaluate 2x. 3y if x. 4 and y. 3.
The Parabola and the Circle
The following are several terms and definitions to aid in the understanding of parabolas.1.) Parabola - A parabola is the set of all points (h, k) that are equidistant from a
fixed line called the directrix and a fixed point called the focus (not on the line.)2.) Axis of symmetry - A line passing through the focus and being perpendicular
to the directrix.3.) The standard equation of a parabola (with the vertex at the origin).
a.) If the Y axis is the axis of symmetry. x 2FOCUS: (0, p) DIRECTRIX: y = - p
b.) If the X axis is the axis of symmetry. y 2FOCUS: (p, 0) DIRECTRIX: x = - p
Example 1: Find the focus and directrix and graph the parabola whose equation is y = -2x 2Solution:
Step 1: Analyze the problem.
Since the quadratic term involves x, the axis is vertical and the standard form x 2 = 4py is used.Step 2: Apply the formula.
The given equation must be converted into the standard form. 2 2 2 2 2 1 2yx y x xy This means that or . 142p1 8p
10,8§·
Therefore the focus (0, p) is and the directrix is 1 8 1 8 yp y yStep 3: Graph.
There exists a line parallel to the directrix and passing through the focus called the primary focal chord, |4p|. This chord may be used to help graph the parabola by determining two points on it. Example 2: Write the standard form of the equation of the parabola with a vertex at the origin and focus at (2, 0). Graph the parabola, including the directrix, the primary focal chord as well as the two points on the graph that they determine.Solution:
Step 1: Analysis.
Since the vertex is at the origin and the focus is at (2, 0): 1.)The axis is horizontal. Therefore the formula y
2 = 4px is used.2.) p =2 because the focus, (p, 0) = (2, 0).
3.) The primary focal chord is |4p| = |(4)(2)| = 8
Step 2: Find the standard equation.
Since p =2 then:
y 2 = 4pxquotesdbs_dbs3.pdfusesText_6[PDF] 9 elements of culture in sociology
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