Graphing Quadratic Functions
04.00
Diposting oleh Melany Christy
Identify the following to graph quadratic functions:
- Axis (or Line) of symmetry
- Maximum or minimum
- y-intercept
- any x-intercept(s)
Axis of Symmetry
Before you begin, click on More Images to view Line of Symmetry, Minimum Point, and y-intercept of y= x^2 + 6x + 5.
Remember, the standard form of a quadratic function is
y = ax2 + bx + c, where a ≠ 0.
The formula for the axis of symmetry is
x = .
2a
Find the axis of symmetry for
y= x2 + 6x + 5.
1. Label a and b.
a= 1, because 1 is the coefficient of x2
b= 6, because 6 is the coefficient of x
2. Plug the numbers into the axis of symmetry formula.
x= -(6)
2(1)
3. Simplify.
x= -6
2
x= -3
4. Draw the line x= -3. Notice that along this vertical line, every value of x is -3.
Vertex: Maximum or Minimum?
2 quick tips for the vertices:
- If the coefficient of a is positive, then the graph opens upward.
- If the coefficient of a is negative, then the graph opens downward.
Because positive 1 is the coefficient of a, the graph opens upward and its vertex is a minimum. The minimum point is a coordinate in the form (x,y). The value of the line of symmetry is always the x-value of the vertex. To find the y-value for the vertex, follow these steps:
1. Plug the x-value into the function.
y= x2 + 6x + 5
y= (-3)2 + 6(-3) + 5
2. Simplify.
y= 9 + -18 + 5
y= -4
3. Plot the minimum, (-3, -4).
Finding the y-intercept
The y-intercept is where the parabola intersects the y-axis. This is also the point at which x=0.
1. Let x=0 in the function and find y.
y= x2 + 6x + 5
y= (0)2 + 6(0) + 5
2. Simplify.
y= 0 + 0 + 5
y= 5
3. Plot the y-intercept, (0, 5).
Use the Quadratic Formula to Find the x-intercepts
Each quadratic function will have two, one, or no x-intercepts.
The most consistent method of finding any x-intercept is the quadratic formula.
Click on More Images for the picture of Quadratic Formula and Graph of x-intercepts. Follow the steps to find any x-intercepts for y= x2 + 6x + 5.
Notice that the x-intercepts are located at (-1,0) and (-5,0).
Final Step (Yes!)
Connect the dots for a perfect parabola. Click on More Images> for the graph of y= x2 + 6x + 5.
Other Article
- Combining Like Terms
- SAT Math Practice 1: Answers and Explanations
- SAT Math Practice 1: Answers and Explanations
- Quadratic Solving
- Simplifying with Exponents Answers and Explanations
- Simplifying with Exponents (2)
- Simplifying with Exponents
- Calculate Slope With a Formula
- Gaussian elimination
- Binary operation
- Commutative algebra
- Field theory (mathematics)
- Ring theory
- Group theory
- Abstract algebra
- Elementary algebra
- Algebraic function
- Algebraic extension
- Algebraic element
- Algebraic solution
- Collection Articles Mathematic
- Party Acquaintances
- Algebraic Structure of Complex Numbers
- Algorithm for Computing the LCM
- Combining Like Terms
- SAT Math Practice 1: Answers and Explanations
- SAT Math Practice 1: Answers and Explanations
- Mulitplying Polynomials Answers and Explanations
- Quadratic Solving
- Simplifying with Exponents Answers and Explanations
- Simplifying with Exponents (2)
- Simplifying with Exponents
- Calculate Slope With a Formula
- Graph theory
- Combinatorics
- Discrete mathematics
- Number line
- Mathematics education
- Gaussian elimination
- Binary operation
- Commutative algebra
- Field theory (mathematics)
- Ring theory
- Group theory
Posting Komentar