Algebra: Chapter 13, Lesson 4, page 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!
Two of tonight’s homework problems solved by MrE are here! Just click it.
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Algebra 1a: CST Review – Area of a Parallelogram, Triangle and Trapezoid
Definitions: `b` is the base and `h` is the height of the geometric figure below. Remember too, that the base and the height are at RIGHT ANGLES to each other!
Area, of a Triangle, `A = (b*h)/2` which is the same thing as `(1/2) * b * h`
Area of a Parallelogram, `A= b*h`.
Area of a Trapezoid, `A = (1/2) * h * (b_1 + b_2)` which is the same thing as `[h * (b_1 + b_2)]/2`
Algebra 1a: CST Review – Equalities and Inequalities – GRAPHING
In graphing equalities and inequalities in x (number line) and x-y graphs, remember to use a T-chart for x-y graphs and to reverse the sign when graphing inequalities when dividing or multiplying by a negative number.