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4 years ago

How to find the maximum or minimum value of a quadratic function?

Mathematics

1 answer:

kipiarov [429]4 years ago

6 0

Answer:

Vertex form

Step-by-step explanation:

You convert to vertex form a(x - b)^2 + c . The coordinates of the maxm/minm will be (b, c).

For example find minimum value of x^2 + 5x - 6:-

x^2 + 5x - 6

= (x + 2.5)^2 - 6.25 - 6

= (x + 2.5)^2 - 12.25

The coordinates of minimumm will be (-2.5, -12.25) The values of the minimum of the function is -12.25

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Y=x^2-6x+3 help write the vertex form of the equation

Artist 52 [7]

Answer:

$y=(x-3)^2-6$

Step-by-step explanation:

$y=x^2-6x+3$

This is written in the standard form of a quadratic function:

$y=ax^2+bx+c$

where:

ax² → quadratic term
bx → linear term
c → constant

You need to convert this to vertex form:

$y=a(x-h)^2+k$

where:

(h,k) → vertex

To find the vertex form, you need to find the vertex. For this, use the equation for axis of symmetry, since this line passes through the vertex:

$x=-\frac{b}{2a}$

Using your original equation, identify the a, b, and c terms:

$a=1\\\\b=-6\\\\c=3$

Insert the known values into the equation:

$x=-\frac{(-6)}{2(1)}$

Simplify. Two negatives make a positive:

$x=\frac{6}{2} =3$

X is equal to 3 (3,y). Insert the value of x into the standard form equation and solve for y:

$y=3^2-6(3)+3$

Simplify using PEMDAS:

$y=9-18+3\\\\y=-9+3\\\\y=-6$

The value of y is -6 (3,-6). Insert these values into the vertex form:

$(3_{h},-6_{k})\\\\y=a(x-3)^2+(-6)$

Insert the value of a and simplify:

$y=(x-3)^2-6$

:Done

6 0

3 years ago

Why did the physiocrats oppose mercantilism?

Alexxandr [17]

Answer:

Mercantilism allowed for government regulation of trade, which interfered with natural market forces.

7 0

3 years ago

Does this parabola have a maximum or minimum value?<br> y=-9(x-4)2-3

lara [203]

Answer:

I think it is a maximum value.

5 0

3 years ago

a dealer sells a camera to a man and makes 15% profit. The man sells the camera to another man for 414$ with 10% loss. Find the

WARRIOR [948]

Answer:

$386.75

Step-by-step explanation:

First we must find the price of the camera after the man sold it, with the 10% loss.

To do this we find 10% of 414, which is 41.4 . Meaning the camera was originally bought from the dealer for $455.40, as we have to add the 10% back onto the price.

Now we find 15% of 455 and subtract it, with 15% being 68.25, the original cost was $386.75. My guy was seriously ripped off :(.

<h2>Orignal price: $386.75</h2>

6 0

3 years ago

2 square root of 5 is between...<br> A) 2 and 3<br> B) 4 and 6<br> C) 6 and 9<br> D) 9 and 12

Natalija [7]

B
Because 2 sqrt5 is = to sqrt 20.

4^2=16, 6^2=36

7 0

3 years ago

Read 2 more answers