How do you illustrate
quadratic equation
in one variable?​

Step-by-step explanation:

Quadratic Equation

Quadratic equation is in the form

ax2+bx+c=0

Where

a, b, & c = real-number constants

a & b = numerical coefficient or simply coefficients

a = coefficient of x2

b = coefficient of x

c = constant term or simply constant

a cannot be equal to zero while either b or c can be zero

Examples of Quadratic Equation

Some quadratic equation may not look like the one above. The general appearance of quadratic equation is a second degree curve so that the degree power of one variable is twice of another variable. Below are examples of equations that can be considered as quadratic.

1. 3x2+2x−8=0

2. x2−9=0

3. 2x2+5x=0

4. sin2θ−2sinθ−1=0

5. x−5x−−√+6=0

6. 10x1/3+x1/6−2=0

7. 2lnx−−−√−5lnx−−−√4−7=0

For us to see that the above examples can be treated as quadratic equation, we take example no. 6 above, 10x1/3 + x1/6 - 2 = 0. Let x1/6 = z, thus, x1/3 = z2. The equation can now be written in the form 10z2 + z - 2 = 0, which shows clearly to be quadratic equation.

Roots of a Quadratic Equation

The equation ax2 + bx + c = 0 can be factored into the form

(x−x1)(x−x2)=0

Where x1 and x2 are the roots of ax2 + bx + c = 0.

Quadratic Formula

For the quadratic equation ax2 + bx + c = 0,

x=−b±b2−4ac−−−−−−−√2a

See the derivation of quadratic formula here.

The quantity b2 - 4ac inside the radical is called discriminat.

• If b2 - 4ac = 0, the roots are real and equal.

• If b2 - 4ac > 0, the roots are real and unequal.

• If b2 - 4ac < 0, the roots are imaginary.

Sum and Product of Roots

If the roots of the quadratic equation ax2 + bx + c

= 0 are x1 and x2, then

Sum of roots

x1+x2=−ba

Product of roots

x1x2=ca

You may see the derivation of formulas for sum and product of roots here.

Which of the following can you add/subtract?

A) 5√4 + 6√4

B) 3√7 − 3√5

C) 9 √ + 39√

Is -3/4 rational or irrational

Able has a younger sister and an older brother.

- Able’s age can be represented by x.
- Able’s sister is 4 years younger than him.
- Able’s older brother is twice as old as he is.
- The combined age of all three siblings is 32.

How old is Able’s younger sister?

9 years

13 years

5 years

3 years

Plz help
2.
The midpoint of AB is M. If the
coordinates of M are (,-2) and
the coordinates of B are (6,1),
what are the coordinates of A?
a) (-5,-5)
b) (2, -10)
c) (-10, 2)
d) (-13/4,-3/2
e) (-5,5)

5(2x-3)=24

Help me in this pleasee

An Ice cream machine fills cartons at a rate of 1440 pints per hour. How many gallons are filled per minute? 1 gal is equal to 8 pints.

The next train will arrive in 32 minutes and 30 seconds.

In how many seconds will the next train arrive?

A Toy Story poster is enlarged. The new length is 5 feet and the width is 3 feet. The original length was 6 inches what was the width?

4x-6>6x-20 solve for the inequality

John purchased a carr in 1961 for $12,000. Experts estimate that its value will increase by 5% per year. How much will be the cost of the car after 22 years
A- 35103$ B- 27600$
C- 10000$ D- 30105$

Proving Triangles congruent: ASA, AAS, SAS SSS
Cate:
For each problem give the correct naming order of the congruent triangles Write that name in order on the
lines for the problem number (see box at bottom) Aso indicate which postulate or theorem is being used
2
AVAVAV
N
ASC.
ABC a
by
LABCO

Jeff earns money mowing lawns. His earnings and hours worked represent a direct variation. He worked for 5 hours and earned $37.50. Determine the constant of proportionality for dollars earned per hours worked and for hours worked per dollars earned.

Which table shows a proportional relationship ?? Pls help

What is the slope of this graph?
A. −4
B. −14
C. 14
D. 4
(picture down below)

Whats 0.52 / 0.0013?

Suppose you had two circular objects. Let the first circular object have a diameter of 26 cm and let second circular object have a diameter that is half as long as the diameter of the first. What would the circumference be for the second item in centimeters?

5) 2-X = 15
Find the value of x

Need help ASAP
Please

what is 2.6 divided by 0.4

bob can draw 14 shapes in 7 minutes how long does it take bob to draw 28 shapes at the same rate

Calculate (2.2 x 10^2 g^3) (2.8 x 10^3 g) put it into standard notation please ​

Will give brainliest will give brainliest will give brainliest and 60 think point

Can someone help me? It's only 2 questions and I will give you 20 points and brainliest!

Please help giving 10 points!
Which statements about the graphs of the equations y = 2x + 4 and y = −x + 4 are true? Select all that apply.

A. The graphs intersect the x-axis at the same point.

B. The graphs intersect the y-axis at the same point.

C. The graphs have different slopes.

D. The graphs are parallel lines.

Evaluate the function f(x) = sec(x - ) for x = 0.

Can someone please help me with these 50 points I just don't get it I need help?

OK, this question is a little complicated. Solve v, 5/v=7.25

You typed a 600 word essay in 12 minutes. Let w be the number of words you can type in one minute. Can w be 60?

Is the difference of 18 and 3 a rational number?

I HAVE 5 MINUTES PLZ HELP ! (its a slope problem)