Creating and Graphing Equations Using Vertex Form Adapted from Walch Education

Vertex Form Standard form, intercept form, and vertex form are equivalent expressions written in different forms. Vertex form: f(x) = a(x – h)2 + k, where the vertex of the parabola is the point (h, k) To identify the vertex directly from an equation in vertex form, identify h (the x-coordinate of the vertex) and k (the y-coordinate of the vertex).

5.3.3: Creating and Graphing Equations Using Vertex Form Practice # 1 Determine the equation of a quadratic function that has a minimum at (–4, –8) and passes through the point (–2, –5). 5.3.3: Creating and Graphing Equations Using Vertex Form

Substitute the vertex into f(x) = a(x – h)2 + k. Vertex form f(x) = a[x – (–4)]2 + (–8) Substitute (–4, –8) for h and k. f(x) = a(x + 4)2 – 8 Simplify. 5.3.3: Creating and Graphing Equations Using Vertex Form

5.3.3: Creating and Graphing Equations Using Vertex Form Substitute the point (–2, –5) into the equation from step 1 and solve for a. f(x) = a(x + 4)2 – 8 Equation –5 = a[(–2) + 4]2 – 8 Substitute (–2, –5) for x and f(x). –5 = a(2)2 – 8 Simplify. –5 = 4a – 8 3 = 4a 5.3.3: Creating and Graphing Equations Using Vertex Form

Substitute a into the equation f(x) = a(x – h)2 + k. The equation of the quadratic function with a minimum at (–4, –8) and passing through the point (–2, –5) is 5.3.3: Creating and Graphing Equations Using Vertex Form

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