Question 428818: How do you find line of symmetry,y intercept, x-intercepts, maximim/minimum point from an quadratic equation to plot the parabola without using a graphing calculator and only using the equation?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! How do you find line of symmetry, y intercept, x-intercepts, maximim/minimum
point from an quadratic equation to plot the parabola without using a graphing calculator and only using the equation?
:
All these can be calculated from the equation: y = ax^2 + bx + c
:
An example would be the easiest to understand, a simple quadratic equation:
y = x^2 - 2x - 8
:
The y intercept is the easiest, this occurs when x = 0, so we have:
y = 0^2 - 2(0) - 8
y = -8 is the y intercept
:
The x intercepts occur when y = 0
0 = x^2 - 2x - 8
We usually write it
x^2 - 2x - 8 = 0
This will factor to
(x-4)(x+2) = 0
Two solutions
x = 4
and
x = -2, these are the x intercepts
:
There is a simple formula for finding the axis of symmetry x = -b/(2a)
In this equation a=1, b=-2
x = 
x = 
x = +1 is the axis of symmetry
:
To find the min/max
The rule for that
If the coefficient of x^2 is positive, it's a minimum
If the coefficient of x^2 is negative, it's a maximum
:
To find the y value for the min in this equation, substitute the axis of symmetry, x=1 and find y
y = 1^2 - 2(1) - 8
y = 1 - 2 - 8
y = -9
Minimum occurs at x=1, y=-9
:
:
To plot this on graph paper, the y intercept (0.-8), the x intercepts (-2,0) and (4,0) The minimum (1,-9)
Finish the graph by plotting the x values between the intercepts -1 to +4
:
Should look like this:
:
Hope this helps you in this
|
|
|
