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).