1. Creating and Graphing Equations Using Vertex Form
Adapted from Walch Education

2. 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).

3. 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

4. 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. 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

6. 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

7. Ms. Dambreville
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