Chapter 5: Q. 15 (page 441)

Use the method of completing the square and what we know about transformations of graphs to show that the vertex of the parabola $f (x) = x^{2} - 3 x + 5 is the point (\frac{3}{2}, \frac{11}{4})$

Short Answer

Expert verified

The graph of parabola is $y = x^{2}$ which is translating $\frac{3}{2}$ units to the right and $\frac{11}{4}$ units up.

Step by step solution

Step 1. Given Information

The given function is $f (x) = x^{2} - 3 x + 5$

Step 2. Explanation

Complete the square of the given function in order to make the function as an equation of parabola.

$y = x^{2} - 3 x + 5 y = {(x - \frac{3}{2})}^{2} + \frac{11}{2}$

Thus, the graph of parabola is $y = x^{2}$ which is translating $\frac{3}{2}$ units to the right and $\frac{11}{4}$ units up.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Use the method of completing the square and what we know about transformations of graphs to show that the vertex of the parabola $f (x) = x^{2} - 3 x + 5 is the point (\frac{3}{2}, \frac{11}{4})$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Discrete Mathematics

Mechanics Maths

Calculus

Pure Maths

Geometry

Study anywhere. Anytime. Across all devices.

Use the method of completing the square and what we know about transformations of graphs to show that the vertex of the parabola f(x)=x2-3x+5isthepoint32,114

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Discrete Mathematics

Mechanics Maths

Calculus

Pure Maths

Geometry

Study anywhere. Anytime. Across all devices.

Use the method of completing the square and what we know about transformations of graphs to show that the vertex of the parabola $f (x) = x^{2} - 3 x + 5 is the point (\frac{3}{2}, \frac{11}{4})$