Sample content WEEK 4 DISCUSSION QUESTIONS PART 1 1. How might the intercepts of a quadratic function be computed? Solution: Y intercept: put x = 0 then we will simply get the y point and the y intercept will be that point and it is written as (0,y1) where y1 is the point we found by putting x = 0 To calculate the x intercept put y = 0 and find the roots of the quadratic equation If the roots are real then it will intersect the x axis (or we will have x intercept), after finding the roots x intercept will be (x1,0) and (x2,0) To explain the whole process lets take an example: Y=x2-5x+6 To find the y intercept put x = 0 We get y = 6 Therefore y intercept (0, 6) Now to find x intercept put y = 0 X2-5x+6=0 X2 -3x-2x+6=0 X(x-3)-2(x-3)=0 (x-3)(x-2)=0 Therefore roots = 2, 3 Or x intercept = (2, 0) and (3, 0) Note: that there are various ways to find the roots of the quadratic equation It can find by using graph, by using formula or factorizing it direc

1. MATH 209 Week 4 Discussion question DQs PART 1 OF 2
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Sample content
WEEK 4 DISCUSSION QUESTIONS PART 1
1. How might the intercepts of a quadratic function be computed?
Solution:

2. Y intercept: put x = 0 then we will simply get the y point and the y intercept will be
that point and it is written as (0,y1) where y1 is the point we found by putting x = 0
To calculate the x intercept put y = 0 and find the roots of the quadratic equation
If the roots are real then it will intersect the x axis (or we will have x intercept), after
finding the roots x intercept will be (x1,0) and (x2,0)
To explain the whole process lets take an example:
Y=x2-5x+6
To find the y intercept put x = 0
We get y = 6
Therefore y intercept (0, 6)
Now to find x intercept put y = 0
X2-5x+6=0
X2 -3x-2x+6=0
X(x-3)-2(x-3)=0
(x-3)(x-2)=0
Therefore roots = 2, 3
Or x intercept = (2, 0) and (3, 0)
Note: that there are various ways to find the roots of the quadratic equation
It can find by using graph, by using formula or factorizing it directly
2. In the case of a quadratic function, what is the number of x and y intercepts the
function may have?

3. Solution:
The graph of a quadratic function will always have one y-intercept and can have
as many as two x-intercepts (remember that intercepts are points where a graph
crosses an axis). The y-intercept is the point where the graph crosses the y-axis so
it will be the value of the function at x = 0. Since f(0) = c, the y-intercept is the point
(0,c). The x-intercept(s), if there are any, are the points where the graph crosses
the x-axis. They can be found by substituting y with 0 and solving the resulting
quadratic equation ax2 + bx + c = 0 for x. This equation has one, two, or no
solutions. When it has one solution, there will be one x-intercept; when there are
two solutions, there will be two x-intercepts and when the equation has no solution,
the graph will have no x-intercepts.
3. What is the meaning of “axis” in regards to a quadratic function?
Solution:
A quadratic function graphs as a parabola. Said parabola has an axis of symmetry
that intersects the vertex (extreme point) of the curve. The two roots of the function,
if they exist, are symmetrically located about this axis.
4. Present a method of graphing a quadratic function. Demonstrate your method.
Solution:
Quadratic Functions A quadratic function has the form
f (x) = ax2 + bx + c
Where a, b and c are real numbers and a is not equal to 0.
The domain of thi
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