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Properties of the Graph of Quadratic Functions
Did you enjoy the activity? To better understand the properties of the graph of a quadratic functions, study some key concepts below.
properties of the graph of quadratic functions
properties of the graph of quadratic functions
The graph of a quadratic function y=ax^2 +bx + c is called a parabola.
If the value of a > 0, the parabola opens upward and has a minimum point.
If the value of a < 0, the parabola opens downward and has a maximum point.
It has a turning point called vertex which is either the highest or the lowest point of the graph. If the function is of the form y= a(x-h)^2 + k, the vertex is the point (h,k).
There is a line called axis of symmetry which divides the graph into two parts such that one-half of the graph is a reflection of the other half. The line x=h is the equation of the axis of symmetry and k is the minimum or maximum value of the function.
The domain of a quadratic function is the set of all real numbers.
The range depends on whether the parabola opens upward or downward. If it opens upward, the range is the set {y : y > k}; if it opens downward, the the range is the set {y : y < k}.
Write your name on your clock. Make an appointment with 12 of your classmates, one for each hour on the clock. Be sure you both record the appointment on your clock. Make an appointment only if there is an open slot that hour on both your clock.
Activity 4: Clock partner activity
Activity 4: Clock partner activity
use your clock partner to discuss the following questions.
use your clock partner to discuss the following questions.
TIME : TOPICS/QUESTIONS TO BE DISCUSSED / ANSWERED
2:00 How can you describe the graph of a quadratic function?
5:00 Tell something about the axis of symmetry of a parabola.
12:00 When do we say that the graph has a minimum/maximum value or point?
3:00 What does the vertex imply?
4:00 How can you determine the opening of the parabola?
6:00 How would you compare the graph of y=a(x-h)^2 + k and that of y= ax^2?
11:00 How would you compare the graph of y= X^2 +k with that of y= ^2 when the vertex is above the origin? below the origin?
1:00 How do the values of h and k in y = a (x - h)^2 + k affect the graph of y = ax^2?
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