Question

Select the correct answer from each drop-down menu. a student rewrites the equation of a parabola to identify the parabola’s vertex. the student made an error when she . correcting this error will .

Answer 1

The student is working on identifying the vertex of a parabola by rewriting its equation. An error was made in the process, which needs correction to correctly determine the vertex. The steps involve using known values, the correct equation, and algebraic manipulation such as completing the square.

Step-by-step explanation:

The question relates to the process of rewriting the equation of a parabola to identify its vertex. The student likely made an error when completing one of the steps necessary for rewriting the equation. Correcting the error would result in accurately determining the vertex of the parabola. The steps involved typically include: identifying known values, identifying the unknown, choosing the correct equation, and then plugging in the known values to solve for the unknown.

To rewrite a parabola equation in vertex form, the process normally involves completing the square or using the vertex formula. Once the correct vertex form y = a(x-h)^2 + k is achieved, where (h, k) is the vertex of the parabola, the vertex coordinates can be easily read off from the equation.

Answer 2

The student made an error when she completed the square. Correction of this error will be y = -4(x - 1/2)² + 1.

Step-by-step explanation:

The student has followed the process of completing the square to rewrite the equation of a parabola in vertex form. By adding and subtracting 1/4 inside the parentheses, the student obtains the vertex form of the equation, which correctly reveals the vertex of the parabola as (1/2, 1/4).

However, the student made an error when she did not distribute the 4 correctly across all terms after completing the square. The corrected equation should be y = -4(x - 1/2)² + 1. Correcting this error will result in the accurate vertex form, which will characterize the parabola correctly.

Your question is incomplete but most probably your full question was

Select the correct answer from each drop-down menu. A student rewrites the equation of a parabola to identify the parabola's vertex.

4x^2-4x+y=0

4x^2-4x=-y

4(x^2-x)=-y

4(x^2-x+ 1/4 )=-y+ 1/4

4(x- 1/2 )^2=-y+ 1/4

-4(x- 1/2 )^2+ 1/4 =y

Vertex: ( 1/2 , 1/4 )

The student made an error when she _____. Correcting this error will _______.