All categories

2 years ago

Describe how to derive the quadratic formula from a quadratic equation in standard form

Mathematics

2 answers:

Ipatiy [6.2K]2 years ago

8 0

Firstly we learn the standard quadratic equation,

ax²+bx+c=0

where a,b,c are real numbers.

Now solve the quadratic equation using the Complete the square method.

Rewriting part of the equation as a perfect square trinomial. If you complete the square on the generic equation ax² + bx + c = 0 and then solve for x,

ax²+bx=-c

x² + $\frac{b}{a} x$ =-c

add both the side $(\frac{b}{2a} )^{2}$

x² + $\frac{b}{a} x$ + $(\frac{b}{2a})^{2} = -\frac{c}{a} + (\frac{b}{2a})^{2}$

$(x+\frac{b}{2a})^{2} = \frac{b^{2}-4ac}{4a^{2}}$ `

take square root both the side

$x = \frac{-b+\sqrt{b^{2}-4ac}}{2a}$

$x= \frac{-b-\sqrt{b^{2}-4ac}}{2a}$

Advocard [28]2 years ago

4 0

Answer:

The quadratic formula is derived from a quadratic equation in standard form when solving for x by completing the square. The steps involve creating a perfect square trinomial, isolating the trinomial, and taking the square root of both sides. The variable is then isolated to give the solutions to the equation.

Step-by-step explanation:

You might be interested in

If 2 less than or equal too X less than or equal too 6, which of the following has the greatest value

vitfil [10]

From the list of choices that you have provided, √x + 2 is the greatest value.

I honestly don't see what 2 < x < 6 has to do with anything.

8 0

3 years ago

Read 2 more answers

Round 835.411 to the nearest tenth.

kondor19780726 [428]

The tenth position is the one that goes after the decimal point.

To round a number, you have to take into account the following:

1. If the number that goes after the position we are going to round to is greater than 5, we round to the next number in that position.

2. If the number that goes after the position we are going to round to is less than 5, we round to the same number in that position.

In this case, the number that is on the tenth's position is 4. The number that is after this position is 1, which is less than 5, then we round the number in this positon to 4.

The rounded number would be:

$835.4$

4 0

1 year ago

Try Again

Rus_ich [418]

Answer:
12 inches
step-by-step explanation:
16 inches of wire = 48 cents
48/16
3 cents for each
36/3
12 inches

4 0

2 years ago

Find the exact value of cos 120° in simplest form with a rational<br> denominator.

IRINA_888 [86]

Given:

cos 120°

To find:

The exact value of cos 120° in simplest form with a rational denominator.

Solution:

We have,

$\cos 120^\circ$

It can be written as

$\cos 120^\circ=\cos (90^\circ+30^\circ)$

$\cos 120^\circ=-\sin 30^\circ$ $[\because \cos (90^\circ-\theta)=-\sin \theta]$

$\cos 120^\circ=-\left(\dfrac{1}{2}\right)$ $[\because \sin 30^\circ=\dfrac{1}{2}]$

$\cos 120^\circ=-\dfrac{1}{2}$

Therefore, the exact value of cos 120° is $-\dfrac{1}{2}$ .

7 0

2 years ago

Without using technology, describe the end

victus00 [196]

Answer:

Up on the left, up on the right

Step-by-step explanation:

The given function is:

$f(x)=3x^{4}+8x^{2}-22x+43$

The degree of f(x) is 4 i.e. an even degree and the leading coefficient i.e. coefficient with highest powered variable is positive in sign.

The graph of a function with even degree always open on same side from both ends. This depends on the sign of leading coefficient what will be the direction of both ends. The positive sign indicates upward opening and negative sign indicates downward opening.

Since, the leading coefficient of f(x) is positive, it will open towards up from both right and left side. So, the correct option is the fourth option.

7 0

2 years ago