Mathematics College

What are the features of the quadratic function ƒ(x) = (x – 3)(x + 7)?

Question 8 options:

A)

Vertex = (2,25), y-intercept = (0,21), x-intercepts = (7,0) and (–3,0), axis of symmetry is x = 2

B)

Vertex = (–2,–25), y-intercept = (0,–21), x-intercepts = (–7,0) and (3,0), axis of symmetry is x = 2

C)

Vertex = (–2,–25), y-intercept = (0,–21), x-intercepts = (–7,0) and (3,0), axis of symmetry is x = –2

D)

Vertex = (–2,25), y-intercept = (0,21), x-intercepts = (7,0) and (3,0), axis of symmetry is x = –2

Answers

Answer 1

Answer:

Option C:Vertex = (–2,–25), y-intercept = (0,–21), x-intercepts = (–7,0) and (3,0), axis of symmetry is x = –2

Step-by-step explanation:

We are given the function;

f(x) = (x - 3)(x + 7)

The axis of symmetry in a quadratic equation is given by the formula;

x = -b/2a

Expanding the function given, we have;

f(x) = x² + 4x - 21

a = 1

b = 4

c = - 21

Thus;

Axis of symmetry is:

x = -(4)/(2 × 1)

x = -2

Now, y-intercept is when x = 0

Thus;

f(0) = (0 - 3)(0 + 7)

f(0) = - 3 × 7 = - 21

y - intercept is (0, - 21)

x-intercept is when f(x) = 0

Thus;

(x - 3)(x + 7) = 0

Thus;

x - 3 = 0 or x + 7 = 0

x = 3 or x = - 7

x - intercept is (-7, 0) and (3,0)

The y-coordinate of vertex will be at the line of axis of symmetry.

Thus, we will put x = -2 into the function to get;

y = (-2 - 3)(-2 + 7)

y = -5 × 5 = - 25

Vertex is at (-2, -25)

Correct Answer is option C

Answer 2

Answer:

Vertex = (–2,–25), y-intercept = (0,–21), x-intercepts = (–7,0) and (3,0), axis of symmetry is x = –2

Step-by-step explanation:

Related Questions

How much money will it cost to buy the paint? Show all work

Answers

Answer:

Step-by-step explanation:

Circle:

diameter = 30 ft

r = 30/2 = 15 ft

Area = πr²

= 3.14 * 15*15

= 706.50 square feet

Triangle:

base (b) = 30 ft

height (h) = 20 ft

Area = [tex]\frac{1}{2}bh[/tex]

[tex]=\frac{1}{2}*30*20\\\\=30*10[/tex]

= 300 square feet

Area of four triangles = 4 * 300

= 1200 square feet

Area to be painted blue = area of circle + area of 4 triangles

= 706.50 + 1200

= 1906.50 square feet

Area painted by one bucket blue paint = 350 sq. feet

Number of paint buckets needed = 1906.50 ÷ 350

= 5.44

= 6

6 buckets of blue paint is needed.

Cost of 6 buckets of blue paint = 85.50 * 6

= $ 513

Each part of the design needs two coats.

So Cost for two coats = 2 * 513

= $ 1026

Square:

Side = 40 ft

Area of square = side *side

= 40*40

= 1600 sq. ft

Area of square to be painted yellow = area of square - area of circle

= 1600 - 706.50

= 893.50 sq.ft

Area painted with one bucket of yellow paint = 250 sq. ft

Number of yellow paint buckets needed = 893.50 ÷ 250

= 3.574

= 4

4 buckets of yellow bucket is needed

Cost of 4 buckets of yellow bucket = 64.50 * 4

= $ 258

Each part of the design needs two coats.

So Cost for two coats = 2 * 258

= $ 516

n= 9c-80 solve for c. if n= 19 what is the value of c?

Answers

Answer:

Step-by-step explanation:

n = 9c - 80

n = 19

19 = 9c - 80

-9c = -80 - 19

-9c = -99

c = 99 / 9

c = 11

Hope this helps

plz mark as brainliest!!!!!!

Arrange the steps to solve the equation V3+3-V23-1= -2.

-Simplify to obtain the final radical term on one side of the equation.

-Raise both sides of the equation to the power of 2.

-Apply the Zero Product Rule.

-Use the quadratic formula to find the values of x.

-Simplify to get a quadratic equation

-Raise both sides of the equation to the power of 2 again.

Answers

Answer:

1. Raise both sides of the equation to the power of 2.

2. Simplify to obtain the final radical term on one side of the equation.

3. Raise both sides of the equation to the power of 2 again.

4 . Simplify to get a quadratic equation.

5. Use the quadratic formula to find the values of x.

Which expression represents a quadratic expression in complete factored form?

A. (x+4)(x-3)
B. (x-1)(3x-9)
C. (2x+4)(x+3)
D. (x-2) + (x+3)

ANSWER PLSSSSSSSSSSSSS, thanks.

Answers

Answer:

A. (x+4)(x-3)

Step-by-step explanation:

1. B. ΔJKE ≅ ΔLYE because SAS.

2. E. No enough information to prove the triangles are congruent.

What is the SAS Theorem?

The SAS theorem is a triangle congruence theorem which states that two triangles which have two pairs of corresponding sides that are congruent and a pair of corresponding included angles that are congruent are congruent triangles.

1. Based on the SAS theorem we can conclude that: B. ΔJKE ≅ ΔLYE because SAS.

2. In the triangles given, we are only given that they have two pairs of corresponding congruent sides. No known congruent sides were given. Therefore, we don't have enough information. The answer is: E. No enough information to prove the triangles are congruent.

Learn more about SAS theorem on:

https://brainly.com/question/2102943

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Please answer this for me :)

Answers

Answer:

d = 1.5

Step-by-step explanation:

yes

Answer:

1.5

Step-by-step explanation:

First put like terms on one side:

-3/8d - 1/2d = -11/16 - 5/8

then make the demominators the same:

-3/8d - 4/8d = -11/16 - 10/16

add up the terms:

-7/8d = -21/16

solve for d:

d= 1.5

can you guy help me quick wit this please

Answers

The second answer is right because when you multiply -2 by 7 and -y it should be -14 and 2y

what is the value of the expression if m=2 and n-6?

Answers

Answer:

where is the expression

Step-by-step explanation:

（＾_＾）（＾_＾）（＾_＾）

which set of order pairs represents a function?

Answers

Answer:

3rd line

Step-by-step explanation:

400 reduced by twice my age is 68 how old am i

Answers

hope it helps.........

16. (a) Find the Highest Common Factor (HCF) of 30 and 42.

Answers

Answer: 6

Step-by-step explanation: By checking the factors of both numbers, you see that 6 is their greatest common factor.

30: 1, 2, 3, 5, 6, 10, 15, 30

42: 1, 2, 3, 6, 7, 14, 21, 42

Hope this helps!

Simplify each of the following powers of i.
i^99

Answers

Answer:

i= sqrt (-1)

If the power is

- even then the value could be -1 or 1

-odd then the value could be -i or i

99 is odd so now is

-i if (99+1)/2 is even or is

i is (99+1)/2 is odd

Now check (99+1)/2= 100/2= 50,

50 is even so

i^99 = -i

Step-by-step explanation:

Give the person brainliest

Alex has to fill his 10 gallon fish tank with water. He only has a 1 pint bucket. How many times will he have to fill his bucket to fill the tank?

Answers

Answer:

Step-by-step explanation:

8 pints in a gallon so then you multiply 8 x 10 and get 80

80 pints fills 10 gallons

Fiecare dintre cei 180 de elevi ai unei școli vorbește cel puțin una dintre limbile germană și engleză . Dintre aceștia, 92 vorbesc limba germană și 130 vorbesc limba engleză. *
Numărul elevilor care vorbesc ambele limbi sunt in numar de
Elevii care vorbesc numai germana sunt în număr de
Elevii care vorbesc numai engleza sunt în număr de

Answers

A histogram shows the frequencies of data in different intervals. So, you cannot read individual values off a histogram alone. With a detailed enough dot plot, you could get very close to the actual team payrolls for each league. A histogram does not give this precision.

Step-by-step explanation:

Plato sample answer

Which statements are true about points A, B, and C? Check all that apply.

Answers

Answer:

Step-by-step explanation:

Answer:

2 & 5

Step-by-step explanation:

please help ! i would mark brainliest to the first answer.

Answers

x^2 = 4 py

where p<0

Step-by-step explanation:

I think this is it but I am not sure

What is equal to d? I’m sorry but I need help.

Answers

answer: -9/13

(picture below shows how to solve it)

A one dimensional object with no endpoint is a?
A.ray
B.line segment
C.line
D.point

Answers

Answer:

its line fjfjfjjejjdjdj

As per the given condition, the required one dimensional object with no end point is a line.

What is a ray?

"In geometry, a ray can be defined as a part of a line that has a fixed starting point but no end point. It can extend infinitely in one direction.

On its way to infinity, a ray may pass through more than one point. When naming a ray, it is denoted by drawing a small ray on top of the name of the ray. "

What is a line segment?

"A line segment is a part of a line that is bounded by two distinct end points, and contains every point on the line that is between its endpoints."

What is a line?

"A line is a one-dimensional object, which has length but no width. A line is made of a set of points which is extended in opposite directions infinitely. It is determined by two points in a two-dimensional plane. "

What is a point?

"A point is a primitive notion that models an exact location in the space, and has no length, width, or thickness. In modern mathematics, a point refers more generally to an element of some set called a space."

Given, a one dimensional object with no endpoint.

Therefore, the require object is a line.

Learn more about a line here: https://brainly.com/question/27560536

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if a person ran 1/2 of a mile in 1/10 of an hour. How far will the person run in one (1) hour?

Answers

Step-by-step explanation:

In 1/10 of 1hr = 1/2 mile

10*(1/10) of 1hr = 10(1/2) mile

(10/10) of 1hr = (10/2) mile

1 of 1hr = 5mile

It says, he can run 5 miles in 1 hour

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