Over 2 (from vertex)
Over 1 (from the vertex)
UP 1
UP 2
UP 3
UP 0.5
DOWN 0.25
UP 4
UP 8
UP 12
UP 2
DOWN 1
y=x²
y= 2x²
y= 3x²
y= o.5²
y= -1/4x²
GRAPHING
Factored Form (y=a(x-s)(x-r)
-You'd find out the x-intercepts first by looking at your equation. The s and r values are the intercepts. (s,0) (r,0)
-Next you'd figure out the axis of symmetry by adding s and r then dividing the sum by 2.
-After that you'd solver for your optimal value by subbing in the axis of symmetry (x) into the equation.
-The vertex will be the (Axis of symmetry, Optimal value)
Vertex Form (y=a(x-h)² + k)
- The vertex is already given to you in the equation!
(h,k)
-Now that you know your vertex you can easily start to find your other points by using the step pattern. (Given above)
Standard Form (y=ax² + bx + c)
-You'd need to find the x intercepts first so you would use the Quadratic formula.
( Bottom of page)
-Then you'd use the step pattern (Given above) to get the rest of the points.
To determine the direction of opening keep in mind that if the a value is negative the parabola opens downwards and if the a value is positive, it opens upwards. (Like a smiley face)