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Chapter 3: Problem 54

Describe how to find a parabola's vertex if its equation is expressed in standard form. Give an example.

Short Answer

Expert verified
For a parabola expressed in standard form \(y = a(x - h)^2 + k\), the vertex is given by the coordinates (h, k). In the example equation \(y = 2(x - 3)^2 + 4\), the vertex is (3, 4).

Step by step solution

01

Understanding the standard form

A parabola in its standard form is expressed as \(y = a(x - h)^2 + k\). In this equation, 'a' determines the shape of the parabola, either opening upwards or downwards. The vertex of the parabola is represented by the coordinates (h, k).
02

Identifying 'h' and 'k'

In the standard equation, (h, k) are the values that constitute the vertex. Therefore, to figure out the parabola's vertex, simply identify the values of 'h' and 'k' in the equation.
03

Example

Take for example the equation \(y = 2(x - 3)^2 + 4\). To determine the vertex of this parabola, identify 'h' and 'k'. Here, 'h' equals to 3 and 'k' equals to 4. Therefore, the vertex is (3, 4).

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