For an equation of the form ax^2 + bx+ c = 0, where the graph crosses the y-axis once and does not intersect the x-axis. Describe the solution(s) of the equation.
(picture)

Answers

Answer 1

Answer:a

Step-by-step explanation:

Answer 2

The solution to the equation ax² + bx + c = 0 , has a graph that crosses the y-axis once and does not intersect the x-axis, then the equation has one real root and two complex conjugate roots that lie on either side of the axis of symmetry.

What is Quadratic Equation?

A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

The roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

where ( b² - 4ac ) is the discriminant

when ( b² - 4ac ) is positive, we get two real solutions

when discriminant is zero we get just one real solution (both answers are the same)

when discriminant is negative we get a pair of complex solutions

Given data ,

Let the quadratic equation be represented as A

Now , the value of A is

If the graph of the equation ax² + bx + c = 0 crosses the y-axis once, it means that the equation has one real root. This is because when x = 0, the equation becomes:

c = 0² + 0 + c = c

Therefore, the point (0, c) is on the y-axis, which means the graph crosses the y-axis once.

If the graph does not intersect the x-axis, it means that the discriminant b² - 4ac is negative. This is because the discriminant determines the nature of the roots of a quadratic equation, and when it is negative, the roots are complex (not real) and the graph does not intersect the x-axis.

So, the solution(s) of the equation ax² + bx + c = 0 are:

x = (-b ± √(b² - 4ac)) / 2a

Since the discriminant is negative, the term inside the square root is negative, and there are no real solutions for x. Instead, the solutions are complex conjugates of the form:

x = (-b ± i√(4ac - b²)) / 2a

where i is the imaginary unit. Since the real part of these solutions is -b/2a, which is the axis of symmetry of the parabola, and the parabola does not intersect the x-axis, the complex roots will be a conjugate pair that lie on either side of the axis of symmetry.

Hence , the quadratic equation is solved

To learn more about quadratic equations click :

https://brainly.com/question/25652857

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Related Questions

30 points for this one, thank you.

Answers

the value of the output is 16

Answer:

Step-by-step explanation:

i though i knew it but i cant figerit out

HELP!! Picture below (ignore the other question

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Answer:

Step-by-step explanation:

Answer:

m ≤ -20

Step-by-step explanation:

-20and all the numbers less than -20 are a solution. I know that -20 is included because the point on it is solid. If the point was hollow the answer would be m < -20

Name the Complimentary Pair?

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angle C & A are the complimentary pair!

HELP PLS THANKSSSSSSSSS

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Answer:

I think it is 2,304

Step-by-step explanation:

I think it’s 2,304 because you have to multiply 8x6x8x6

Write a two-step equation that involves division and
addition and has a solution of x = -25

Answers

Answer: look at the image for the answer and the explanation

Step-by-step explanation:

Equation: X+Y= Z
Z= -30

Answer: X= -25
Y= -5
Z= -30

6.5/40.3 = M/12.4 what dose m =

Answers

m=2

[tex] \frac{6.5}{40.3} = \frac{m}{12.4} [/tex]

[tex]40.3m \: = 6.5 \times 12.4[/tex]

[tex]m = \frac{6.5 \times 12.4}{40.3} [/tex]

[tex]m = \frac{80.6}{40.3} [/tex]

[tex]m = 2[/tex]

Answer:

M = 2

Step-by-step explanation:

What does it mean to have something be equal (Equivalent)?

Equivalence means to be same, whether it be value, temperature, size, etc.

If equivalence means to be the same, we can use this equation to figure out what M is equal to.

40.3 ÷ 12.4 = 3.25

So, in order to solve for M, we need to divide 6.5 by 3.25.

6.5 ÷ 3.25 = 2

Therefore, M = 2.

FIRST QUESTION
9 POINTS and BRAINLIEST

MAGDIEJAMESNY!!!

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Answer:

Step-by-step explanation:

Answer:

HI!

I love how we are friends

U R A GOOD FRIEND!

Step-by-step explanation:

Evaluate (whith steps) -3 - 5 (8 + 4) + 16 - 32

Answers

Answer:

Using the order of operations (PEMDAS), we evaluate the expression as follows:

First, we perform the operations inside the parentheses: 8 + 4 = 12.

Next, we multiply 5 by 12: 5(12) = 60.

Then, we combine the like terms: -3 - 60 + 16 - 32 = -79.

Therefore, -3 - 5 (8 + 4) + 16 - 32 = -79.

The answer is -79 ( I think )

help me with this topic pls

Answers

Answer: 235.5 yd^3

Step-by-step explanation:

Step 1. Find the radius.Remember the formula; pi * r^2 * h/3

Since the diameter is 2 times the radius, d=10, we have to split it by 2 {10/2 =5}

Step 2. Simplify. 3.14 * 5^2 * 9/3

Step 3. PEMDAS, start with exponents. 3.14 * 25 * 9/3

Step 4. PEMDAS, divide the numbers.

3.14 * 25 * 3
Step 5. Multiply 25 * 3.

3.14 * 75

Step 6. Simplify. 235.5 yd^3

Answer:

235.5 yd^3

Step-by-step explanation:

Find the slope and the y-intercept of the graph of the linear equation. y= -2x - 1

Answers

Answer:

slope = -2

y-intercept = -1

Step-by-step explanation:

for y = -2x - 1

Using the slope intercept formula y = mx + b, then slope m = -2 and y-intercept is (0,b) or (0,-1)

Y=mx+ c
M=Slope or Gradient
C=Y-intercept

(M) Slope= -2
(C) Y- intercept= -1

What is 2. 8×4. 6 find the missing partial products

Answers

—> 12.88 <—

A N S W E R

the answer would be 12.88
hope this helps

i need help on the (b.) part pls thanks

Answers

Answer:

Column 1 choose option 1 (x,y) --> (3/2x,3/2y)

Column 2 choose option 2 (x,y) --> (3/2x,3/2y)

Step-by-step explanation:

Focus on just Point S to go from (6,2) to (9,3) you would multiply 6*3/2 and 2*3/2. So, the scale factor is 3/2.

Answer:Column 1: 1 (x,y) --> (3/2x,3/2y)

Column 2: 2 (x,y) --> (3/2x,3/2y)

What is the surface area of the prism shown?

Answers

Answer: 1.8
Explanation: you need to find the area of each of the sides of the shape and then add them together so the sum is:
(0.5x1.2)+(0.4x1.3)+(0.4x1.2)+(0.5x0.4)
=1.8
Note: to find the area of the triangle you don’t need to divide by two because there are two of the triangle sides so they just cancel out.
Hope this helps, pls mark brainiest answer.

please help me with this

Answers

Answer:

Below

Step-by-step explanation:

The last choice is false....linear functions can have positive or negative slopes

the answer is false i believe

helpp mee please asap please

Answers

A and B is the answer everything less than 20

Answer:

A and B.

Step-by-step explanation:

Since 18 is less than 20, A is correct.

Since 12 is less than 20, B is correct.

C and D are not correct because they are larger than 21.

Hope it helped!

hey guys my little brother needs help can you help out?
568.50 x 0.2
need help asap!!!!

Answers

Answer:113.7

Step-by-step explanation:

Answer:

113.7

Step-by-step explanation:

To calculate 20% of 568.50, you can convert 20% to a decimal by dividing it by 100.

20% ÷ 100 = 0.20

Then, you can multiply the decimal by the original value to find the answer:

0.20 x 568.50 = 113.70

Therefore, 20% of 568.50 is 113.70.

he table below shows how much money you have in savings each week. Answer the questions below

x (Week) y (Savings)

0 $50
1 $75
2 $100
3 $125
4 $150
5 $175

B. How much money did you start with?

Answers

Answer:

According to the table, you had $50 in savings at the beginning, during Week 0.

You started with $50 and you had that during week 0.

OKAY I NEED HELP ASAP,

THE PROBLEM IS , y divided by 6 x 6 = 3 x 6

SO THEN ITS ASKING ME "IF WE DIVIDED BY 6 AND THEN MULTIPLY BY 6, WHat IS LeFT???

PLEASE HEP ME

Answers

Answer:

Step-by-step explanation:

y divided by 6x6=3x6

1. multiply first

a) 6x6 = 36

b) 3x6=18

c) y/6 times 6 =3 x6 .....make it a fraction Y over 6 times 6 over 1

d) y/6 times 6/1----cross off the two 6's

Now: y=3x6

y=18

6 times 6 = 36 and 6 times 3 = 18

36 = 18

So, 18 divided by y = 36

so, 18 times 36 = 648

Hence, y is divided by 648 to get 6 x 6

Show work. Due in 5 hours.

Answers

Answer:

Part A:

6 feet

Part B:

Around 9.17 feet

Part C:

Around 3 feet

Step-by-step explanation:

Part A:

The Pythagorean Theorem (which is a^2 + b^2 = c^2), is the simpilist way to solve this. a = 8; c = 10. so, the problem becomes (64 + b^2 = 100). Subtract 64 from both sides to get (b^2 = 36). Square root both sides to get (b = 6).

Part B:

Using the same method, but with different measurements:

(a^2 + b^2 = c^2)

(16 + b^2 = 100)

(b^2 = 84)

(b = 9.17)

Part C:

The difference of 9.17 and 6 is 3.17. Therefore, the closest foot is 3. Hope this helps! Have a great day! :)

PART A uses Pythagoras. Because you are finding the short side you do 8 squared and 10 squared (100 and 64) and subtract them to get 36. You then do the square root of 36 to get 6 which is the answer!

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For an equation of the form ax^2 + bx+ c = 0, where the graph crosses the y-axis once and does not intersect the x-axis. Describe the solution(s) of the equation. (picture)

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For an equation of the form ax^2 + bx+ c = 0, where the graph crosses the y-axis once and does not intersect the x-axis. Describe the solution(s) of the equation.
(picture)