Which function in vertex form is equivalent to f(x) = x² + 6x + 3?
Answer: The equivalent function in vertex form is f(x) = (x + 3)² – 6.
Vertex Form of a Quadratic Function
The vertex form of a quadratic function is y = a(x – h)² + k, where (h, k) is the vertex. To convert f(x) = x² + 6x + 3 to vertex form, complete the square by adding and subtracting (6/2)² = 9 inside the function: f(x) = (x² + 6x + 9) – 9 + 3, resulting in f(x) = (x + 3)² – 6. This form is useful in identifying the vertex and analyzing the properties of the parabola.
FAQ on Vertex Form of a Quadratic Function
What is the vertex of a function in vertex form?
The vertex is the point (h, k) in y = a(x – h)² + k.
How do you convert standard form to vertex form?
Complete the square and rewrite the equation in vertex form.
Why is the vertex form useful?
It provides a direct way to identify the vertex and the direction of the parabola.
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