Algebra 1

Carter, Cuevas, Day, Holiday, Luchin

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 801 pages

ISBN: 9780078884801

Chapter 9: Q52. (page 532)

Graph the function.
$y = 鈭� 3 x^{2} + 6 x 鈭� 4$

Short Answer

Expert verified

The graph of the function $y = 鈭� 3 x^{2} + 6 x 鈭� 4$ is

Step by step solution

Step 1. Define the standard form of the quadratic function.

A quadratic function, which is written in the form, $y = a x^{2} + b x + c$ , where, $a 鈮� 0$ is called the standard form of the quadratic function.

Step 2. Define the maximum or minimum point of the function y=ax2+bx+c.

The graph of the function $y = a x^{2} + b x + c$

Opens upward and has a minimum value at $x = 鈭� \frac{b}{2 a}$ , when $a > 0$ .

Opens downward and has a maximum value at $x = 鈭� \frac{b}{2 a}$ , when $a < 0$ .

Step 3. y-intercept of the function y=ax2+bx+c.

The $y$ -intercept of the function $y = a x^{2} + b x + c$ is always at $y = c$ .

Step 4. Plot the graph of the function y=−3x2+6x−4.

Compare the quadratic function $y = 鈭� 3 x^{2} + 6 x 鈭� 4$ with the standard quadratic function $y = a x^{2} + b x + c$ .

$a = 鈭� 3, 鈥� b = 6, 鈥� c = 鈭� 4$

Substitute $a = 鈭� 3$ and $b = 6$ in $x = 鈭� \frac{b}{2 a}$ .

$x = 鈭� (\frac{6}{2 (鈭� 3)}) x = 鈭� (\frac{6}{鈭� 6}) x = 1$

Since, $a < 0$ .

So, the graph opens downward and has a maximum value at $x = 1$ .

The $y$ -intercept is $y = c$ .

The graph of the function $y = 鈭� 3 x^{2} + 6 x 鈭� 4$ is shown below.

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Graph the function.
$y = 鈭� 3 x^{2} + 6 x 鈭� 4$

Short Answer

Step by step solution

Step 1. Define the standard form of the quadratic function.

Step 2. Define the maximum or minimum point of the function y=ax2+bx+c.

Step 3. y-intercept of the function y=ax2+bx+c.

Step 4. Plot the graph of the function y=−3x2+6x−4.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Theoretical and Mathematical Physics

Discrete Mathematics

Decision Maths

Probability and Statistics

Statistics

Study anywhere. Anytime. Across all devices.

91影视

Graph the function.y=鈭�3x2+6x鈭�4

Short Answer

Step by step solution

Step 1. Define the standard form of the quadratic function.

Step 2. Define the maximum or minimum point of the function y=ax2+bx+c.

Step 3. y-intercept of the function y=ax2+bx+c.

Step 4. Plot the graph of the function y=−3x2+6x−4.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Theoretical and Mathematical Physics

Discrete Mathematics

Decision Maths

Probability and Statistics

Statistics

Study anywhere. Anytime. Across all devices.

Graph the function.
$y = 鈭� 3 x^{2} + 6 x 鈭� 4$