• Slides: 12

Quadratic Graphs and Their Properties. Quadratic Functions. n r a e l l l ’ u o ty a h W To graph quadratic functions of the form To identify the axis of symmetry, vertex, domain. range and intercept(s) for a given parabola. To graph quadratic functions of the form y Quadratic function, Standard form, r a l u b a c o V Parent function, parabola, axis of symmetry, vertex, minimum, maximum

Take a Note: A quadratic function is a function that can be written in the form This form is called the standard form of a quadratic function. Examples: The simplest quadratic function the quadratic parent function. is The graph od the quadratic function is called parabola and has a U shape. You can fold a parabola so that the two sides match exactly. The fold or line that divides the parabola into matching halves is called the axis of symmetry.

Problem 1: Graphing a Quadratic. Identifying a vertex. Graph. Step 1: Make a table. X -2 4 -1 1 0 0 1 1 2 4 3 9

Step 2: Plot the points a)(-2, 4) (-1, 1) (0, 0) (1, 1) (2, 4) b)(-2, -8) (-1, -2) (0, 0) (1, -2) (2, -8) c)(-2, 5) (-1, 3. 5) (0, 3) (1, 3. 5) (2, 5)

Take a note: The highest or the lowest point of a parabola is a vertex, which is on the axis of symmetry

Your turn: A child drops a pebble from a height of 30 ft above a lake. The function gives the height h of the pebble (in feet) after t seconds. What is the graph of this quadratic function? At about what time does the pebble hit the water?

Take a note: There is another way to graph a parabola . The graph of has the line as its axis of as symmetry . , where The x-coordinate of the vertex is and the y-coordinate of the vertex is . You can use the coordinates of the vertex, the axis of symmetry and the y-intercept (meaning when x=0)to help you graph a quadratic function.

Problem 3: What is the graph of ? Step 1: Identify a, b, and c. Step 2: find the vertex, remember the x-value is the axis of symmetry. Step 3: The y-intercept Step 4: Find another point in the side as the vertex.