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Chapter 13: Problem 111

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The graph of \(x=a(y-k)+h\) is a parabola with vertex at \((h, k)\)

Short Answer

Expert verified
The initial statement is false. The correct statement is: The graph of \(x=a(y-k)^2+h\) is a parabola with a vertex at \((h, k)\).

Step by step solution

01

Identify the standard form of a parabola

The standard form of a parabola's equation is \(y=a(x-h)^2+k\) for parabolas that open up or down, or \(x=a(y-k)^2+h\) for parabolas that open right or left, where \((h, k)\) is the vertex of the parabola.
02

Compare the given equation with the standard form

The equation given is \(x=a(y-k)+h\). It is not in either standard form. We can, however, rearrange it into the standard form \(x=a(y-k)^2+h\).
03

Correct the false statement

The graph of \(x=a(y-k)^2+h\) is a parabola with a vertex at \((h, k)\). Note the square on \((y-k)\) which was missing in the original statement.

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Most popular questions from this chapter

Use the vertex and intercepts to sketch the graph of each equation. If needed, find additional points on the parabola by choosing values of y on each side of the axis of symmetry. $$x=-3 y^{2}-6 y$$

How can you distinguish ellipses from hyperbolas by looking at their equations?

Will help you prepare for the material covered in the next section. Solve: \(x^{2}=2(3 x-9)+10\)

Use the vertex and intercepts to sketch the graph of each equation. If needed, find additional points on the parabola by choosing values of y on each side of the axis of symmetry. $$x=(y-2)^{2}+3$$

Use the vertex and the direction in which the parabola opens to determine the relation's domain and range. Is the relation a function? $$x=y^{2}-2 y-5$$
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