Algebra: Chapter 12-4, p 552
Quadratic Functions
A quadratic function is defined by `f(x) = ax^2 + bx + c`. To make it easier, just replace the `f(x)` with `y` and treat as you have done in the past.
With a function in standard form `ax^2 + bx + c`, the vertex is `-b/(2a)` and the axis of symmetry is `x = -b/(2a)`. The vertex is the point on the PARABOLA where the slope changes sign from positive to negative or vice-versa. The axis of symmetry, you recall, is the line when the parabola can be “flipped” or “folded over” and still be symmetrical in shape.
You should plot at least 5 points when making a graph of the equation and DO NOT use a ruler to connect the points, this is a parabola, NOT a linear equation.
Where the parabola crosses the x-axis are called the ROOTS of the equation. You can find the ROOTS easily by setting y = 0 and solving the quadratic equation with the factoring techniques from Chapter 6 and 10.
Math-8: Chapter 12-1, p 612
Area: Parallelograms, Triangles and Trapezoids
The are of a rectangle is the length * width or `l⋅w`.
A parallelogram is a rectangle sometimes pushed to one side. The area of a parallelogram is then `b⋅h ` where b is the base and h is the height. The height and the base MUST be perpendicular to each other.
The area of a triangle is `1/2(b⋅h)` where b is the base again and h is the height. Again, the base and the height must be perpendicular.
A trapezoid has 2 bases, one is `b_1` and the other is `b_2`. A trapezoid has a height perpendicular to the 2 bases. The formula for the area of a trapezoid is `1/2(h)(b_1+b_2)`.
Remember, the base of a triangle can be any side, just make sure that the height is perpendicular! The same is true for a parallelogram, don’t use the slant height, it must be perpendicular. In a trapezoid, the bases MUST BE PARALLEL!