Reviewed by Jessica Kaminski
What is the first step when rewriting y = 6x² + 18x + 14 in the form y = a(x – h)² + k?
Answer: The first step when rewriting y = 6x² + 18x + 14 in the form y = a(x – h)² + k is to factor out the 6 from the x² and x terms
Rewriting a quadratic equation from the standard form y = ax² + bx + c to the vertex form y = a(x – h)² + k helps easily identify the vertex of the parabola. The process often involves factoring and completing the square. The first crucial step is to factor out the coefficient of x² from the quadratic and linear x terms.
Methods
Math Tutor Explanation Using the Factoring Method
To prepare the quadratic for completing the square, start by factoring out the leading coefficient from the x terms.
Step 1: Identify the coefficient 'a' in the x² term, which is 6
Step 2: Factor out 6 from both x² and x terms in the equation
Math Tutor Explanation Using the Completing the Square Method
The process of rewriting a quadratic in vertex form involves preparing the quadratic and linear terms for completing the square.
Step 1: Group the x² and x terms together
Step 2: Factor 6 from the x² and x terms to set up for completing the square
Step 1:
Step 2: field_63f47597ecdfc
Math Tutor suggests: Practice Rewriting Quadratic Equations in Vertex Form
Build your skills in converting quadratic equations to vertex form and understanding completing the square with these related exercises.
FAQ on Converting Quadratics to Vertex Form
Why do I factor out the leading coefficient before completing the square?
Factoring out the leading coefficient ensures the x² term has a coefficient of 1, which is necessary for correctly completing the square.
Can I complete the square without factoring out the coefficient first?
Completing the square is easiest and most accurate if you first factor out the coefficient of x².
What does the vertex form of a quadratic represent?
The vertex form y = a(x – h)² + k gives the vertex of the parabola at (h, k) and shows the direction of opening.
What should I do after factoring out the leading coefficient?
After factoring, proceed to complete the square with the terms inside the parentheses, then adjust the constant term to maintain the equation's balance.
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