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).

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# Example 1: Find the equation of the quadratic with the graph: