Quadratic Relations
By: Harman Saini
What is Parabola?
What are the quadratic relations?
Vertex form y = a(x - h)2 + k
- Axis of symmetry
- Optimal Value
- X-intercepts
What is the axis of symmetry?
How do you find the axis of symmetry?
To find your Axis of Symmetry you would need to look at the h value, in the vertex form.
In the equation y= -2(x-2)2+5 the h value which is -2, turns into a positive and will become your axis of symmetry. You would write you axis of symmetry like: x= 2.
What is the optimal value?
How do you find the optimal value?
What is the x-intercepts?
How to find the x-intercepts?
Example:
y=-2(x-2)2+6
0=2(x+2)2+6
-6=2(x+2)2
-6/2=(x+2)2/2
-3=(x+2)2
+-3=x+2
-3=x+2
-3-2=x
-5=x
-3=x+2
-3-2=x
-1=x
How to graph a parabola in vertex form?
Factored Form y=a(x-r)(x-s)
- Axis of symmetry
- Optimal Value
- Zero/x-intercept
How to find the axis of symmetry?
To find the axis of symmetry in factored form, you must first take the numbers inside the brackets out. In this equation y=(x-4)(x-6) you must change the signs of the numbers in the bracket (-4 will become 4 and -6 will become 6). After that you must add the two number together and divide it by two, which would give your axis of symmetry as 5.
How to find the optimal value?
To find the optimal value in factored form, you must first sub in the axis of symmetry into the x variables in the brackets and then solve for y, which will give you your optimal value.
Example:
y=(x-4)(x-6)
y=(5-2)(5-6)
y=(3)(-1)
y=-3
Optimal value= -3.
How to find the zeros/x-intercepts?
How to graph in factored form?
Standard Form y=ax^2+bx+c
- Axis of symmetry
- Optimal Value