Quadratic Functions Quadratic Expressions Quadratic Equations Definition A
- Slides: 27
Quadratic Functions, Quadratic Expressions, Quadratic Equations Definition: A quadratic function is a function of the form where a, b, c are real numbers and a 0. The expression on the right-hand-side is call a quadratic expression.
Quadratic Expressions: Factored Form Examples: 1. 2.
Factoring quadratic expressions: Given integers. Case 1: a = 1; Since where a, b, c are
we have
Examples:
Case 2: integers and a 1. Since where a, b, c are
we have
Examples:
Quadratic Equations: A quadratic equation is an equation of the form: Problem: Find the real numbers x, if any, that satisfy the equation. The numbers that satisfy the equation are called solutions or roots.
Methods of Solution: Method 1: Factor then the solutions (roots) of the equation are
Examples:
Method 2: Use the QUADRATIC FORMULA The real number solutions (roots) of the quadratic equation are: provided
The quadratic formula is often written as The number discriminant. is called the
The Discriminant: Given the quadratic equation If:
(1) ; the roots are: (2) the roots are: (3) no real roots.
Examples:
Quadratic Functions: The graph of is a parabola. The graph looks like if a > 0 if a < 0
Key features of the graph: 1. The maximum or minimum point on the graph is called the vertex. The xcoordinate of the vertex is:
2. The y-intercept; the y-coordinate of the point where the graph intersects the yaxis. The y-intercept is: 3. The x-intercepts; the x-coordinates of the points, if any, where the graph intersects the x-axis. To find the xintercepts, solve the quadratic equation
Examples: Sketch the graph of vertex: y-intercept: x-intercepts:
Sketch the graph of Vertex: y-intercept: x-intercept(s):
Sketch the graph of Vertex: y-intercept: x-intercept(s):
- Chapter 9 quadratic equations and functions
- 578x5
- Expressions and equations jeopardy
- System of equations and inequalities unit test
- Expressions equations and inequalities unit test
- Chapter 9 rational expressions and equations answers
- Translating expressions and equations
- Translating equations
- Solving rational equations
- Translate words into equations
- Chapter 1 expressions equations and inequalities
- Chapter 1 expressions equations and inequalities
- Vertical line test
- Quadratic equation by factoring definition
- Rational expressions and functions
- Quiz 7-3 logarithmic and exponential equations
- 4-4 factoring quadratic expressions
- Objectives of factoring
- 9-3 polar and rectangular forms of equations
- Translate word equations to chemical equations
- Inverse circular functions
- Unit 6 radical functions homework 4 rational exponents
- Differential equations with discontinuous forcing functions
- 2-2 linear relations and functions
- Differential equations with discontinuous forcing functions
- Unit 4 lesson 4 factoring to solve quadratic equations
- Quadratic formila
- The area of a rectangular fountain is (x^2+12x+20)