Chapter 6: Q. 6 (page 437)

Use transformations to graph the function $y = {(x - 3)}^{2} + 2$ .

Short Answer

Expert verified

The graph of the function is:

Step by step solution

Step 1. Given Information

The given function is $y = {(x - 3)}^{2} + 2$ and we need to use transformations to graph the function.

Step 2. Simplifying the equation

The equation can be written as:

$y = {(x - 3)}^{2} + 2 \Rightarrow y - 2 = {(x - 3)}^{2}$

Using the transformations we get,

$X \equiv (x - 3) Y \equiv (y - 2) ∴ Y = X^{2}$

Step 3. Finding the vertex

Comparing the equation with the standard formula of parabola $x^{2} = 4 a y$ we get,

Vertex of the parabola $Y = X^{2}$ is $X = 0, Y = 0$ .

$∴ x - 3 = 0 \Rightarrow x = 3 y - 2 = 0 \Rightarrow y = 2$

Vertex of the parabola is $(3, 2)$ .

Step 4. Finding focus of parabola

Focus of the standard parabola is $(0, a)$ .

$∴ 4 a = 1 \Rightarrow a = \frac{1}{4}$

Transforming we get,

$x - 3 = 0 \Rightarrow x = 3 y - 2 = \frac{1}{4} \Rightarrow y = 2 + \frac{1}{4} \Rightarrow y = \frac{9}{4}$

The focus of the parabola is $(3, \frac{9}{4})$ .

Step 5. Graphing the function

The graph of the function is:

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Use transformations to graph the function $y = {(x - 3)}^{2} + 2$ .

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Simplifying the equation

Step 3. Finding the vertex

Step 4. Finding focus of parabola

Step 5. Graphing the function

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Use transformations to graph the functiony=(x-3)2+2.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Simplifying the equation

Step 3. Finding the vertex

Step 4. Finding focus of parabola

Step 5. Graphing the function

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Mechanics Maths

Pure Maths

Probability and Statistics

Applied Mathematics

Calculus

Study anywhere. Anytime. Across all devices.

Use transformations to graph the function $y = {(x - 3)}^{2} + 2$ .