# Draw the graph of each equation and label each vertex: y = − 4 x 2 − 5 x + 9

### Elementary Technical Mathematics

12th Edition
Dale Ewen
Publisher: Cengage Learning
ISBN: 9781337630580

Chapter
Section

### Elementary Technical Mathematics

12th Edition
Dale Ewen
Publisher: Cengage Learning
ISBN: 9781337630580
Chapter 11.4, Problem 17E
Textbook Problem
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## Draw the graph of each equation and label each vertex: y = − 4 x 2 − 5 x + 9

To determine

To graph: The equation y=4x25x+9 and label the vertex.

### Explanation of Solution

Given Information:

The provided equation is y=4x25x+9.

Graph:

Consider the given equation y=4x25x+9.

The general equation of parabola is y=ax2+bx+c. Then, the x coordinate of vertex of parabola is b2a. And, the y coordinate of vertex of parabola is determined by substituting the value of x=b2a in the parabola equation.

Compare the equation y=4x25x+9 with its general form to get;

a=4,b=5 and c=9

So, the vertex of parabola is;

x=b2a=(5)2(4)=58

Put the value of x=58 in the equation y=4x25x+9, to get;

y=4(58)25(58)+9=2516+258+9=25+5014416=6916

The vertex coordinate of the parabola is (58,6916).

In order to graph the equation,

Take some arbitrary points of x to find the value of y;

For x=3,

Put the value of x=3 in the equation y=4x25x+9, to get;

y=4x25x+9=4(3)25(3)+9=4(9)+15+9=12

For x=2,

Put the value of x=2 in the equation y=4x25x+9, to get;

y=4x25x+9=4(2)25(2)+9=4(4

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