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3 years ago

How do you find the minimum value of a quadratic function?

Mathematics

1 answer:

aniked [119]3 years ago

6 0

The minimum value of a function is the place where the graph has a vertex at its lowest point.

There are two methods for determining the minimum value of a quadratic equation. Each of them can be useful in determining the minimum.

(1) By plotting graph

We can find the minimum value visually by graphing the equation and finding the minimum point on the graph. The y-value of the vertex of the graph will be the minimum.

(2) By solving equation

The second way to find the minimum value comes when we have the equation y = ax² + bx + c.

If our equation is in the form y = ax^2 + bx + c, you can find the minimum by using the equation min = c - b²/4a.

The first step is to determine whether your equation gives a maximum or minimum. This can be done by looking at the x² term.

If this term is positive, the vertex point will be a minimum; if it is negative, the vertex will be a maximum.

After determining that we actually will have a minimum point, use the equation to find it.

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PLEASE HELP ME WITH BOTH OF THESE PROBLEMS THIS IS DUE SOON PLEASE HELP ME

iogann1982 [59]

Answer:

Step-by-step explanation:

P = 2width + 2length

8x = 2x + 2 length; 8x-2x = 2 length; 6x=2 length

length = 3x

sides= 1/4 of 3x = 3x/4

perimeter of square = 4* side = 4*3x/4 = 3x

x= 4

P rectangle =8x= 8*4= 32

P square = 3x = 3*4 = 12

32-12 = 20 cm greater is the P rectangle than P of square

A rectangle = 2x*x = 2*4*4 = 32

A square =(3x/4)² = (3*4/4)² = 9

32-9 = 23 cm² greater is the A rectangle than A of square

4Comic+1 Nonfiction

4comic = 8y so 1 comic = 2y

1 nonfiction = (3+7y)+ 2y

1 nonfiction = 7y+2y+3 = 9y+3

total= 8y+9y+3 = 17y+3

if y=4

total = 17*4 +3 = $71

7 0

3 years ago

Read 2 more answers

2x + 12 = 1/3 (7/3x+4/3)

gladu [14]

Answer:

Step-by-step explanation:

2x + 12 = 1/3 (7/3x+4/3)

$2x+12=\frac{1}{3}*\frac{7x}{3}+\frac{1}{3}*\frac{4}{3}\\\\2x+12=\frac{7x}{9}+\frac{4}{9}\\\\2x-\frac{7x}{9}=\frac{4}{9}-12\\\\\frac{2x*9}{1*9}-\frac{7x}{9}=\frac{4}{9}-\frac{12*9}{1*9}\\\\\frac{18x}{9}-\frac{7x}{9}=\frac{4}{9}-\frac{108}{9}\\\\\frac{18x-7x}{9}=\frac{4-108}{9}\\\\\frac{11x}{9}=\frac{-104}{9}\\\\\\x=\frac{-104*9}{11*9}=\frac{-104}{11}=-9\frac{5}{11}$

8 0

3 years ago

The value of a certain car decreases by 16% each year. What is the 1⁄2-life of the car?

svet-max [94.6K]

Answer:

The half life of the car is 3.98 years.

Step-by-step explanation:

The value of the car after t years is given by the following equation:

$V(t) = V(0)(1-r)^{t}$

In which V(0) is the initial value and r is the constant decay rate, as a decimal.

The value of a certain car decreases by 16% each year.

This means that $r = 0.16$

$V(t) = V(0)(1-r)^{t}$

$V(t) = V(0)(1-0.16)^{t}$

$V(t) = V(0)(0.84)^{t}$

What is the 1⁄2-life of the car?

This is t for which V(t) = 0.5V(0). So

$V(t) = V(0)(0.84)^{t}$

$0.5V(0) = V(0)(0.84)^{t}$

$(0.84)^{t} = 0.5$

$\log{(0.84)^{t}} = \log{0.5}$

$t\log{0.84} = \log{0.5}$

$t = \frac{\log{0.5}}{\log{0.84}}$

$t = 3.98$

The half life of the car is 3.98 years.

7 0

3 years ago

13. The manager of a landscaping company collected data for an entire summer. Before each job he completely filled the gasoline

nadya68 [22]

Answer:

Before you get started, take this readiness quiz.

Write as an inequality: x is at least 30.

If you missed this problem, review (Figure).

Solve 8-3y<41.

If you missed this problem, review

5 0

2 years ago

Read 2 more answers

1. Select all values of x that are solutions to the equation: -2(x + 4)(3x - 18) = 0A) -6B) -4C) -2D) OE) 2F) 4G) 6

navik [9.2K]

$\begin{gathered} -2(x+4)(3x-18)=0 \\ \text{There are two factors here which are} \\ -2(x+4)\text{ and} \\ (3x-18) \\ \text{This means, either} \\ 2(x+4)=0 \\ 2x+8=0 \\ 2x=-8 \\ \text{Divide both sides by 2} \\ x=-4 \\ OR \\ 3x-18=0 \\ 3x=18 \\ \text{Divide both sides by 3} \\ x=6 \\ \text{Therefore,} \\ x=-4\text{ or} \\ x=6 \end{gathered}$

x = -4 OR x = 6

The correct options are B and G

6 0

1 year ago