Completed Square Form (Leaving Cert Mathematics): Quizzes

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Completed Square Form
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What is the form of a quadratic in completed square?

y=a(x−h)2+ky=a(x-h)^2+k

What is the first step in completing the square?

Factor out a if a≠1a \neq 1

How do you find the vertex from the completed square?

Identify (h,k)(h,k) from y=a(x−h)2+ky=a(x-h)^2+k

How is the value of hh determined in the form y=a(x−h)2+ky=a(x-h)^2+k?

From the expression (x−h)(x-h)

Why do we add and subtract (b/2a)2(b/2a)^2 during completing the square?

To form a perfect square trinomial

What is the purpose of completing the square?

To find vertex form

In y=2(x+3)2−4y=2(x+3)^2-4, what is the vertex?

(-3, -4)

What is the purpose of the constant kk in y=a(x−h)2+ky=a(x-h)^2+k?

Vertical shift of parabola

How do you convert y=2x2+8x+3y=2x^2+8x+3 into completed square form?

Factor out 2, complete the square inside

What is the completed square form of y=2x2+8x+3y=2x^2+8x+3?

2(x+2)2−52(x+2)^2-5

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