Conic Sections - Ellipse
standard form of the equation of an ellipse:
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standard form of the equation of an ellipse:
Standard Equation: x<sup>2</sup>= 4py y<sup>2</sup>= 4px
vertical parabola horizontal parabola
axis y-axis x-axis
vertex (0,0) (0,0)
p is the focus of p>0 opens up p>0 opens right
the parabola
p<0 opens down p<0 opens left
focus (0,p) (p,0)
Consider two points C(h,k) and P(x,y) ;and the distance between them is r. From the distance formula:
Slope-Intercept Form
If P1(x1, y1)and P2(x2, y2)are two different points, then the slope of the line between them is;
ax2+ bx + c = 0
The quadratic formula is used to solve unfactorable quadratic equations.
The general forms for quadratic inequalities are:
ax2+ bx + c > 0
ax2+ bx + c < 0
ax2+ bx + c >= 0
ax2+ bx + c =< 0
The number line plays an important role in solving factorable quadratic inequalities.
Quadratic Equations (2nd degree equations in one variable. )
Standard form is ax²+ bx + c.
Since a rational expression is the quotient of two algebraic expressions, it can be represented in fractional form. In doing so, it is often desirable to eliminate all terms involving radicals from the denominator of the fraction. This is known as rationalizing the denominator.
EX.
The quadratic expressions considered herein are of the form
ax2 + bx + c
where x is the (only) variable, and a, b and c are nonzero real numbers.
When a = 1, the quadratic expression simplifies to
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