What is the first step when rewriting y = 3x² + 9x – 18 in the form y = a(x – h)² + k?
Answer: The first step is to factor out the coefficient of x² (3) from the first two terms, giving y = 3(x² + 3x) – 18.
Understanding the Vertex Form
Rewriting a quadratic equation in vertex form, y = a(x – h)² + k, involves completing the square. The first step is to factor the leading coefficient (a) from the x² and x terms if a is not 1. This sets the stage for completing the square in the next steps, eventually leading to a form that easily shows the vertex of the parabola represented by the quadratic equation. This technique is crucial in analyzing the properties of quadratic functions and in solving optimization problems.
FAQ on Understanding the Vertex Form
How do you find the vertex of a parabola in standard form?
Convert the equation to vertex form and the vertex will be (h, k).
What is the significance of ‘a’ in the vertex form?
a’ determines the parabola’s opening direction and its width.
Why is completing the square important in converting to vertex form?
Completing the square reveals the vertex of the parabola, making it easier to analyze and graph.
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