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Parabola

Calculus 1 Exam 3 3of4

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Calculus
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Geometry
Algebraic geometry
Conic sections
Analytic geometry
Hyperbola
Focus
Parabola
Ellipse
Semi-major and semi-minor axes
Degenerate conic
Degeneracy
Asymptote

14) Determine whether the equation represents an ellipse, a parabola, a hyperbola, or a degenerate conic. 15) Find the focus, directrix, and focal diameter of the parabola, and sketch its graph. a) b) Vertex: Focus: Directrix:

notecard

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Curves
Parabola

Pe^rt and A=P(1+r/n)^nt (rate, # it compounds per year, years) Pump fill 4hr., 2nd fill 3hr. t/4+t/3=1 multi. By 3, 4, then 12. Cancel base and solve. Or find CD and #?s to make it. Add #?s and / CD by sum. Set de. = 0. Cancels r holes. Stayed r va?s. degree of nu. Higher- no ha. Lower- it?s y=0, x-axis. =, then it?s at y= LC of nu./LC of de. Y-int= c of nu./c of de. Even + S E, Even ? s e (parabola), odd + s E, odd ? S e (line). Think of self as y-axis. Standard dev. = ox on calc. 68, 95,99.7. 95-68/2=13.5. inside + left, - right; outside + up, - down. When (a) is -, graph flips horizontally. If (a)>1, narrower; vice versa (absolute value). |Variable-Given value| = Difference/Error. When = x (-b/2a), what = y (insert x), when hit ground = quad formula.

Parabola Notes

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To derive the focus of a simple parabola, where the axis of symmetry is parallel to the y-axis with the vertex is at (0,0), such as then there is a point (0,f) ? the focus, F ? such that any point P on the parabola will be equidistant from both the focus and the linea directrix, L. The linea directrix is a a line perpendicular to the axis of symmetry of the parabola (in this case parallel to the x axis) and passes through the point (0,-f). So any point P=(x,y) on the parabola will be equidistant both to (0,f) and (x,-f). FP, a line from the focus to a point on the parabola, has the same length as QP, a line drawn from that point on the parabola perpendicular to the linea directrix, intersecting at point Q.

Parabolas

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Algebra
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Conic sections
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Parabolas Graphs a parabola, showing coefficients for the equation in both standard form, y=a(x-h)2+k, and general form, y=ax2+bx+c. How to use || Examples || Other Notes -------------------------------------------------------------------------------- -------------------------------------------------------------------------------- How to use To change the values of the coefficients, use the "+" and "-" buttons under each value. The buttons change the value by 0.1 at each step. Holding a button down causes this action to be repeated. Click the "Clear" button to reset all values to the default values, a=1 and all other values are 0. -------------------------------------------------------------------------------- Examples Horizontal shifts: in standard form,

Parabola

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Parabolas and their functions

Parabolas 1.Normal Parabola f(x) = x? root : (0/0) apex : deepest point/highest point of the parabola 2.Displacement up/down the y-axis f(x) = x?+k root : 1 solution: k = 0 2 solutions: k > 0 0 soltuions: k < 0 apex : (0/k) 3.Displacement on the x-axis f(x) = (x + h)? root = apex : (-h/0) 4. Displacement on x- and y-axis f(x) = a(x+h)? + e root : look at 2. aspex : (-h/k)
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