Asked by Jayla Watson on Mar 10, 2024

Verified

Identify the vertex and focus of the parabola $(x−10)_{2}+36(y+6)=0$ .

A) vertex: $(10,−6)$ focus: $(−154,−6)$

B) vertex: $(10,−6)$ focus: $(10,−15)$

C) vertex: $(10,−6)$ focus: $(154,−6)$

D) vertex: $(−10,6)$ focus: $(−10,−15)$

E) vertex: $(−10,6)$ focus: $(−154,6)$

A) vertex: $(10,−6)$ focus: $(−154,−6)$

B) vertex: $(10,−6)$ focus: $(10,−15)$

C) vertex: $(10,−6)$ focus: $(154,−6)$

D) vertex: $(−10,6)$ focus: $(−10,−15)$

E) vertex: $(−10,6)$ focus: $(−154,6)$

Vertex

A point where two or more curves, lines, or edges meet. In the context of geometry, it is often used to refer to the corner point of a polygon or the apex of a cone or pyramid.

Parabola

The graph of a quadratic function, a U-shaped curve that can open upwards or downwards, determined by the function's coefficients.

Focus

A point used in the definitions of conic sections, such as ellipses and hyperbolas, that helps to define their shapes.

- Determine the specific features of parabolas, including their vertex and focus.

Verified Answer

JC

Jacob Caudill

Mar 10, 2024

Final Answer :

B

Explanation :

The given equation can be rewritten in the form $(x−h)_{2}=4p(y−k)$ to identify the vertex $(h,k)$ and the focus $(h,k+p)$ . Here, $h=10$ , $k=−6$ , and $4p=36$ , so $p=9$ . Thus, the vertex is $(10,−6)$ , and the focus, found by adding $p$ to the $y$ -coordinate of the vertex, is $(10,−6+9)=(10,−15)$ .

## Learning Objectives

- Determine the specific features of parabolas, including their vertex and focus.