Given the vertex ( 4, 6 )and the point(1, -3), write the vertex form equation of the quadratic
function.

Answers

Answer 1

Answer:

[tex]\displaystyle f(x) = -(x-4)^2 + 6[/tex]

Step-by-step explanation:

A given quadratic has its vertex at (4, 6) and the point (1, -3). We want to write the equation in vertex form of the quadratic.

Recall that vertex form is given by:

[tex]\displaystyle f(x) = a(x-h) ^2 + k[/tex]

Where (h, k) is the vertex and a is the leading coefficient.

Since our vertex is at (4, 6), h = 4 and k = 6:

[tex]\displaystyle f(x) = a(x - 4)^2 + 6[/tex]

To determine the leading coefficient, since we are given that (1, -3) is a point on the parabola, when x = 1, y = -3. Substitute and solve for a:

[tex]\displaystyle \begin{aligned} (-3) & = a((1)-4)^2 + 6 \\ \\ -3 & = a(-3)^2 + 6 \\ \\ 9a & = -9 \\ \\ a & = -1 \end{aligned}[/tex]

Hence, the leading coefficient a is -1.

Then our equation in vertex form is:

[tex]\displaystyle f(x) = -(x-4)^2 + 6[/tex]


Related Questions

Do you think school is good or bad why? (Use your own opinion) I just wanna see your guys opinions

Answers

Answer:

its good because it can help u with ur future it is bad because it is early in the morning and u go there tired

Step-by-step explanation:

Answer:

Good and bad

Step-by-step explanation:

Part of it is good since its actually getting me to my dream job. Bad because it causes a lot of stress (for me anyway).

Am I doing this right I’m trying to help my little brother with his math homework but I don’t remember how to do this and he wants me to use the “cake method” (LCM stands for least common multiple)

Answers

Answer:

The least common multiple is 30. Hope that helps!!

Step-by-step explanation:

please help me on this ​

Answers

Answer:

[tex] {36}^{ - \frac{1}{2} } \\ = \frac{1}{ {36}^{ \frac{1}{2} } } \\ = \frac{1}{ \sqrt{36} } \\ = \frac{1}{6} \\ {64}^{ \frac{1}{3} } \\ = {(4 \times 4 \times 4)}^{ \frac{1}{3} } \\ = { {4}}^{ {3}^{ \frac{1}{3} } } \\ = 4 \\ thank \: you[/tex]

how man times can 2 go intp 9

Answers

Answer:

4 times

Step-by-step explanation:

It goes in because 2+2+2+2=8 so you cant add 2 again or else it will go over so there for the answer is 4 times.

If f(x)=(x-3)^2, find f(-4)

Answers

Solution:Given, f(x) = (x-3)^2Therefore, f(-4) = (-4-3)^2= (-7)^2= -7 × -7= 49Answer:

f(-4) = 49.

49

Step-by-step explanation:

f(x) = (x - 3)²

f(-4) = (-4 - 3)²

f(-4) = (-7)²

f(-4) = 49

Is point (90, 68) on line j? Explain how you know​

Answers

I think the answer is A

Can someone do 1-4 for me please i will give brainiest

Answers

Answer:

Step-by-step explanation:

f(4)=5

f(-1)=0

f(0)=1

F(2)=3

24x - 10 = -12x + 40, What would be the coefficient of x if the variables were moved to the left side of the equation?

Answers

Answer:

25/18

Step-by-step explanation:

24x - 10 = -12x + 40

<=> 24x + 12x = 40 + 10

<=> 36x = 50

<=> x = 50/36

<=> x= 25/18

What is the area of the polygon?

Answers

I’m pretty sure it’s 38ft^2


(The area of a quadrilateral is equal to length x width. So the area of the larger part of the polygon would be 32ft^2, the area of the small square is 4ft^2 and I’m assuming the area of the small triangle would be 2ft^2 because it has the same length and width as the small square but since it’s a triangle it’s area would be equal to half the area of the square. 32+4+2=38, so the answer would be 38ft^2.)

please, someone, help me with this. Im giving brainliest!

Answers

Answer:

2x-10=14

2x=10+14

2x=24

x=24/2

x=12.

i guess it cant have infinite solutions.........

false.

May I please receive help?

Answers

9514 1404 393

Answer:

parallel: y = -7x -44perpendicular: y = 1/7x -8/7

Step-by-step explanation:

The given equation is in slope-intercept form:

  y = mx +b . . . . . . line with slope m and y-intercept b

For the purpose of this question, you need to recognize that the line with equation ...

  y = -7x +8

has a slope (x-coefficient) of -7.

The parallel line will have the same slope (x-coefficient).

The perpendicular line will have a slope that is the opposite reciprocal of this:

  m = -1/(-7) = 1/7

Each line will have a y-intercept (b) that makes the line go through the given point. The y-intercept can be found by solving the slope-intercept equation for b:

  b = y - mx . . . . . . where (x, y) is the point you want the line to go through

__

parallel line:

  b = -2 -(-7)(-6) = -2 -42 = -44

The equation of the parallel line is y = -7x -44.

__

perpendicular line:

  b = -2 -(1/7)(-6) = -14/7 +6/7 = -8/7

The equation of the perpendicular line is y = 1/7x -8/7.

(x + 2)(x + 3)(x + 4) can be written in the form x + ax² + bx + c
where a, b and care positive integers.
Work out the values of a, b and c.

Answers

Answer:

[tex]a=9, b=26, c=24[/tex]

Step-by-step explanation:

Let's expand the expression bit by bit.

[tex](x+2)(x+3)=(x)(x)+(x)(3)+(2)(x)+(2)(3)=x^2+5x+6[/tex] by FOIL.

We have that [tex](x^2+5x+6)(x+4)=x(x^2+5x+6)+4(x^2+5x+6)=x^3+5x^2+6x+4x^2+20x+24=x^3+9x^2+26x+24[/tex].

So, the answer is [tex]\boxed{a=9, b=26, c=24}[/tex]

What is Cubic Polynomial?

A cubic polynomial is a type of polynomial with the degree of 3 i.e. the highest exponent of the variable is 3.

The general form of a cubic polynomial is written as p(x): ax³ + bx² + cx + d, a ≠ 0, where a, b, and c are coefficients and d is the constant with all of them being real numbers.

Given:

(x + 2)(x + 3)(x + 4)

Now, Multiplying the monomial

= (x² + 2x + 3x+ 6 ) ( x+4)

=  (x² + 5x+ 6 ) ( x+4)

= x³ + 4x² + 5x² + 20x + 6x+ 24

= x³ + 9x² + 26x+ 24

Now, Comparing it with the standard form of cubic Polynomial

ax³ + bx² + cx + d

So, a= 1, b= 9, c= 26 and d= 24.

Learn more about cubic Polynomial here:

https://brainly.com/question/28081769

#SPJ2

please someone help me with this. Giving brainliest!!

Answers

Step-by-step explanation:

option A is correct

we will add 5 to both the sides

1/8x - 5 = 3

1/8x = 8

than we will multiply 8 to both the sides

x = 8×8 = 64.

hope this answer helps you dear...take care abd may u have a great day ahead...and ur test/exam/assignment also go well!

3 The diagram shows parallel lines a and b cut by
transversals cand d.
If mzi = 115° and m_8 = 105°, what is the measure of
each of the following angles?
56
87
4/3
9 10
13/14
b
Answer: mz5=
t
12 11
16/15
mZ11 =
m2 16 =
Curriculum Associates, LLC
Copring permitted for classroom use
Grade 8 Lesson 9 Understand Angle Relationships
hol narconnel anly Thic rochure ovires on 6/30/2003

Answers

Answer:get the government ewual

Step-by-step explanation:

You have to get the government equal

choosw thw graph that represents the following function :

y=2+4









graph a linear equation with a function table


please help me i will mark as brainlyst

Answers

Answer:

do you mean y=2+4x?

if it is, it would be the top one.

Find the equation of a line that is perpendicular to the line x=-9 and contains the point (-8,1)

Answers

Step-by-step explanation:

the line x = -9 had only one valid x value (-9), but then all values for y between -infinity and +infinity are valid.

does this sound familiar ?

it should, because the y-axis is the same type of line.

it is x = 0.

so, x = -9 is simply parallel to the y-axis.

and any line perpendicular to it (crosses the original line in a right angle = 90 degrees) is then parallel to the x-axis.

there the situation is upside-down: there is only one valid y value, and all values between -infinity and +infinity are valid x values.

since the specified point on that line has y = 1, it means that the whole line is

y = 1

What is the equation of this line?
A. y = -3x + 1
B. y = -3x - 1
C. y = 3x + 1
D. y = 3x - 1

Answers

The correct answer is D. y=3x-1

Please help me find the value of x

Answers

Answer:

60 degree angle

Step-by-step explanation:

If both of thise angles make 180  then you can divide 180 by 3. this give you 60. you would divide by t3 because 2 of the 3 parts go to the 2x angle.  2x means it is double        your welcome

solve the inequality 3x-5<10

Answers

Answer:

answer is 5

Step-by-step explanation:

am 100% sure lol

Answer:

x < 5

Step-by-step explanation:

3x - 5 < 10

[make x the subject of the formula]

3x < 10 + 5

3x < 15

[divide both sides of the equation by 3]

3x / 3 < 15 / 3

x < 15 / 3

x < 5

Which expeession can be simplified as 1/n¹⁸ ?

(n²)⁹

[tex]( {n}^{ - 9}) ^{ - 2} [/tex]
[tex](n^{ - 6}) ^{ - 3} [/tex]
[tex](n^{ - 3}) ^{6} [/tex]

Answers

Step-by-step explanation:

the last one is the correct answer

Solution:

[tex] \frac{1}{ {n}^{18} } \\ = {n}^{ - 18} \\ = {n}^{( - 3 \times 6)} \\ = ( {n}^{ - 3} ) ^{6} [/tex]

Answer:

[tex]( {n}^{ - 3} ) ^{6} [/tex]

the weekly average cost of hiring a caravan in wales is £250
in July the average cost increases to £800
calculate the percentage increase
give your answer in 2 signifcant figures

Answers

9514 1404 393

Answer:

  220%

Step-by-step explanation:

The percentage change is computed by ...

  % change = ((new value)/(old value) -1) × 100%

  = (800/250 -1) × 100% = (3.2 -1) × 100%

  = 220%

The increase was 220%.

helpp pls no random or wrong answers!

Answers

Answer:

a) 2/5, b) 2.5

Step-by-step explanation:

a)

[tex](4/25)^{1/2} = \sqrt{4/25} = 2/5[/tex]

b)

[tex](4/25)^{-1/2}=(25/4)^{1/2}=\sqrt{25/4} =5/2=2.5[/tex]

Step-by-step explanation:

please mark me as brainlest


Could someone help me

Answers

Answer:

A: the answer is 10

B: the answer is 0.03

Step-by-step explanation:

Answer:

a is 10

b is 0.03

hope this helps

What is the value of
( - ) x 43 - ?
A. 6
16
B. 10
C. 35
D. 40

Answers

C.) 35 - skksjsndjsksnsksnns
c) 35 … use PEMDAS in order to get the correct answer !

evaluate the series 2 + 4 + 8 + 16 + 32 + 64

Answers

The series is that each number is doubled and added to the next doubled number

Which graph represents a function.

Answers

Answer:

one on bottom rght

Step-by-step explanation:

what percent of 500is 120

Answers

Answer:

24%

Step-by-step explanation:

Hope this helps :)

Answer:

24% of 500 is 120...........

How would you write 43—% asa decima

Answers

43. Hope that helps

Answer:

if it's -43% it's -0.43. If it's 43% it's 0.43

Step-by-step explanation:

please someone help me. Im giving brainliest ! Correct answers only :)

Answers

[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]

The Correct choice is : D

Here's the solution :

[tex] \sqrt{528} = 22.978250[/tex]

[tex] \sqrt{528} \approx23[/tex]

Which three cards have an equal value

Answers

Answer:

the bottom 3 the bottom left one equals 1.33 altogether and if you count the second one it's also 1.33 or 133 blocks coloured and the last one is also 1.33

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