Quadratic function is an function that can be written in the form f(x)= ax2 + bx + c, where a 0. It is defined by a quadratic expression, which is an expression of the form ax2 + bx + c, where a 0.
The graph of a quadratic function is called a parabola.
Axis of symmetry is a line that divides the parabola into two parts that are mirror images of each other. The vertex of a parabola is either the lowest point on the graph or the highest point of the graph.
Minimum and Maximum Values: Let f(x)= ax2 + bx + c, where a 0. The graph of f is a parabola.
If a > 0, the parabola opens up and the vertex is the lowest point. The y-coordinate of the vertex is the minimum value of f. If a < 0, the parabola opens down and the vertex is the highest point. The y-coordinate of the vertex is the maximum value of f. .
If x2=a and athen x is called a square root of a. If a > 0, the number a has two square roots,a and -/a. The positive square root of a,a, is called the principal square root of a. IF a=0, then0=0. When you solve a quadratic equation of the form x2=a, you can use the rule below:.
Solving Equations of the Form x2=a: If x2=a and a 0, then x=/a or x= -/a, or simply x= +-/a.
Use the Properties of Square Roots below to simplify the resulting square root. Properties of Square Roots: Product Property of Square Roots - if a and b0:ab =a *b. Quotient Property of Square Roots - If aand b > 0: |a/b| = |a| |b|.
Pythagorean Theorem: If ÑABC is a right triangle with the right angle at C, then a2 + b2 = c2/.
Factoring reverses the process, allowing you to write a sum as a product.
Factoring x2 + bx + c: To factor an expression in the form ax2 + bx + c where a=1, look for the integers r and s such that r*s=c and r+s=b. Then factor the expression. x2+bx+c=(x+r)(x+s).
Factoring the Difference of Two Squares: a2-b2=(a+b)(a-b).
Do you agree or disagree with the following statement? It is more important for students to study history and literature than it is for them to study science and mathematics. Use specific reasons and example to support your opinion. Students take lessons in diverse subjects in school. As their g...
Algebra 8 Derek Harms I thought that this semester was easier than what it looked like it would be but it still was hard. I enjoyed the challenge and thought it was very interesting to be in your class. My favorite part was the end of the first quarter when we had to find the mathmatics of dif...
Romans Did and Greeks Thought Life's milestones have been passed through generations and to different cultures since the beginning of time. From the start, people have been able to put their minds together to come up with new and easier ways to do daily activities. These brilliant and deter...
.); the second part -from line 15 to line 21- would rather deal with books (in there, Bacon describes the different types of books that there are); the third part would take from line 21 to line 27, and in that part, Bacon identifies the different sciences with the different skills that those sciences help us acquire: "Histories" make you wise, Mathmatics make you subtle, etc.); finally, the fourth part, which would go from line 27 to the end, can be taken as a conclusion, as quite an optimistic conclusion since it tells that we can make whatever we want to, by means of practice and investigat...
MATHEMATICS IN A BICYCLE The mathematics of a bicycle can be broken down into three can be broken down into three basic types. The design of the frame, deals mainly with geometry. The size of the wheels and the distance they cover deals with multiplication. The gear ratios are found by division. Basically, without the knowledge of mathematics the bicycle would have not been developed or invented. ...
Mathematics education: The relevance of "contextual teaching- in developing countries Mohd. Sahar Sauian, Universiti Teknologi MARA, Malaysia Many studies had shown that rural students are lagged behind in Mathematics compared to their urban counterparts particularly in developing countries. The poor performance recorded is normally associated with negative factors such as learning cultures, poor environment, lack of teachers and other scores of attitudinal problems faced by the students. Teachers in developing countries are also faced with the dilemma of whether to adopt strictly to "conten...
