How do I write the equation of a parabola from its graph? Using a point and the vertex? Notes # ______
Example 1: Find the equation of the quadratic with the graph:
6
Step 1: Write down what you know:
-6
6
Roots: ___________
Axis of Symmetry: ___________
Vertex: _____________
Y-Intercept: ______________
Step 2: You need to find the value of a.
Determine which form you have enough information to use
and simplify.
-6
Work:


y = a(x – h)2 +k
y = a(x – α)(x – β) α ,β are the roots
Step 3: Plug in what you know and solve for a
Step 4: Expand into standard form: y = ax2 + bx + c
Example 2: Find the equation of the quadratic with the graph:
Step 1: Write down what you know:
8
Roots: ___________
Axis of Symmetry: ___________
Vertex: _____________
Y-Intercept: ______________
Step 2: You need to find the value of a.
2
Determine which form you have enough information to use
and simplify.


Work:
y = a(x – h)2 +k
y = a(x – α)(x – β) α ,β are the roots
Step 3: Plug in what you know and solve for a
Step 4: Expand into standard form: y = ax2 + bx + c
How do I write the equation of a parabola from its graph? Using a point and the vertex? Notes # ______
x=1
Step 1: Write down what you know:
16
Roots: ___________
Axis of Symmetry: ___________
Vertex: _____________
Y-Intercept: ______________
Step 2: You need to find the value of a.
Determine which form you have enough information to use
and simplify.
-2
Work:


y = a(x – h)2 +k
y = a(x – α)(x – β) α ,β are the roots
Step 3: Plug in what you know and solve for a
Step 4: Expand into standard form: y = ax2 + bx + c
Example 4: Find, in the form y = ax2 + bx + c, the equation of the quadratic whose graph cuts the x – axis
at 4 and -3 and passes through the point (2, -20)
Example 5: Find, in the form y = ax2 + bx + c, the equation of the quadratic whose graph has a vertex at
(-3, -5) and passes through the point (1, 11).