Log In Start studying!

Select your language

Suggested languages for you:
Answers without the blur. Sign up and see all textbooks for free! Illustration

Q61.

Expert-verified
Algebra 2
Found in: Page 293
Algebra 2

Algebra 2

Book edition Middle English Edition
Author(s) Carter
Pages 804 pages
ISBN 9780079039903

Answers without the blur.

Just sign up for free and you're in.

Illustration

Short Answer

Find the coordinates of the maximum or minimum value of each quadratic equation to the nearest hundredth.

fx=-6x2+9x

The coordinates of the minimum value of the quadratic equation fx=-6x2+9x to the nearest hundredth is 0.75,3.375.

See the step by step solution

Step by Step Solution

Step 1. Given Information.

Given to determine the coordinates of the maximum or minimum value of the quadratic equation fx=-6x2+9x to the nearest hundredth.

Step 2. Explanation.

The maximum or minimum value of a quadratic function lies at the vertex of the graph.

For an equation of the form fx=ax2+bx+c:

If a>0, it is an upwards opening parabola and so has a minimum value

If a<0, it is a downwards opening parabola and so has a maximum value.

So, the given quadratic equation has a maximum value.

For an equation of the form fx=ax2+bx+c, the x-coordinate of the vertex is given by x=-b2a

Here for the given equation, a=-6, b=9

Plugging the values in the equation:

x=b2ax=926x=912x=0.75

Hence the x-coordinate of the vertex is x=0.75.

So, the y-coordinate of the vertex can be obtained by plugging the value in the equation.

Plugging x=0.75 in the equation:

fx=6x2+9xf0.75=60.752+90.75f0.75=3.375+6.75f0.75=3.375

Hence the coordinates of the vertex is 0.75,3.375.

Recommended explanations on Math Textbooks

94% of StudySmarter users get better grades.

Sign up for free
94% of StudySmarter users get better grades.