Algebra: Chapter 13-4, p 589
The Quadratic Formula, finally!
Given that `ax^2 + bx + c = 0`, then the quadratic formula
`x = (−b±sqrt(b^2−4ac))/(2a)`
gives the solutions of the quadratic equation. This requires that the quadratic equation is always in standard form:
- a is the coefficient of the x^2 term
- b is the coefficient of the x term and
- c is the constant
Memorize it and memorize the discriminant, the expression under the radical (the `b^2−4ac` thingy).
- If the discriminant is > 0, then there are 2 real number solutions
- If the discriminant is = 0, then there is just 1 real number solution
- If the discriminant is < 0, then there are NO real number solutions because you don’t know (yet) how to take the root of a negative real number.
Don’t forget that the
- solutions
- answers
- x-intercepts
- roots and
- zeroes
all mean the same thing. By definition, the equation `ax^2+ bx + c=0` implies that we are setting `y = 0 ` and finding the x-intercepts or the roots or the answers or the solutions!!
Once again, Purplemath.com comes to the rescue, check out these examples for the use of the quadratic formula!
Math-8: Chapter 12-6, p 638
Surface Area of Pyramids and Cones
You know how to the do the surface area of pyramids. First, do the area of the base, it can be a square, triangle or even a hexagon like I showed you my deck lamp from the 1700’s-1800’s. Then, you can do the area of the triangles, remembering that the area `a=(1/2)b⋅h`. Multiply the number of FACES by the area of just one of the triangular faces and add it to the base.
For cones, the bottom area is just the area of a circle, `a=πr^2` and the area of the lateral stuff is `a=π⋅r⋅l` where `l` is the slant height of the cone.
Try a couple, you’ll get the hang of it!