Chapter 2, Problem 2RE

### Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Chapter
Section

### Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

# Sketch the graph of the quadratic functions in Exercises 1 and 2, indicating the coordinates of the vertex, the y-intercept, and the x-intercepts (if any). f ( x ) = − x 2 − x − 1

To determine

To graph: The function f(x)=x2x1 and indicate the coordinates of the vertex, the y-intercept, and x-intercept.

Explanation

Given Information:

The provided function is f(x)=āx2āxā1.

Graph:

Consider the function,

f(x)=āx2āxā1

Compare the equation f(x)=āx2āxā1 with the standard function f(x)=ax2+bx+c and find the value of a,b and c.

The values are a=ā1,Ā b=ā1 and c=ā1.

Here a>0, therefore the parabola will be upward facing.

To graph a quadratic function, four things should be calculated first.

(i) Vertex

(ii) x-intercept

(iii) y-intercept

(iv) Symmetry

Vertex: The formula of x-coordinate of a vertex is,

x=āb2a

Substitute a=ā1 and b=ā1 in the equation x=āb2a.

x=ā(ā1)2ā(ā1)=ā12

To find the y-coordinate of the vertex, substitute x=ā12 in the function f(x)=āx2āxā1.

f(x)=ā(ā12)2ā1(ā12)ā1=ā14+12ā1=ā34

Thus, coordinates of the vertex are (ā12,ā34).

To calculate x-intercept of the function, substitute f(x)=0 in the equation f(x)=āx2āxā1 and solve.

āx2āxā1=0

Use the quadratic formula x=ābĀ±b2ā4ac2a to find the roots of the equation

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