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3 years ago

The vertex of this parabola is at (-2, 5). Which of the following could be its equation?

Mathematics

1 answer:

LenKa [72]3 years ago

5 0

Answer:

y=3(x+2)^2+5

Step-by-step explanation:

The vertex is (p, q) where the "p" value is the x-coordinate of the vertex and the "q" is the y-coordinate of the vertex.

Given the vertex (-2, 5) the "p" here is -2 and "q" here is 5, so plugging into the vertex form we get y=3(x+2)^2+5

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3 years ago

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3 years ago

Given the functions f(x) = 4x2 − 1, g(x) = x2 − 8x + 5, and h(x) = –3x2 − 12x + 1, rank them from least to greatest based on the

tangare [24]

Answer:

Option D) h(x), f(x), g(x)

Step-by-step explanation:

we know that

The axis of symmetry of a vertical parabola is equal to the x-coordinate of the vertex of the parabola

Part 1) we have

$f(x)=4x^{2} -1$

This is a vertical parabola open upward

The vertex is a minimum The vertex is the point (0,-1)

The x-coordinate of the vertex is 0

The axis of symmetry is x=0

Part 2) we have

$g(x)=x^{2}-8x+5$

This is a vertical parabola open upward

The vertex is a minimum

Convert the equation into vertex form

$g(x)-5=x^{2}-8x$

$g(x)-5+16=x^{2}-8x+16$

$g(x)+11=x^{2}-8x+16$

$g(x)+11=(x-4)^{2}$

$g(x)=(x-4)^{2}-11$

The vertex is the point (4,-11)

The x-coordinate of the vertex is 4

The axis of symmetry is x=4

Part 3) we have

$h(x)=-3x^{2}-12x+1$

This is a vertical parabola open downward

The vertex is a maximum

Convert the equation into vertex form

$h(x)-1=-3x^{2}-12x$

$h(x)-1=-3(x^{2}+4x)$

$h(x)-1-12=-3(x^{2}+4x+4)$

$h(x)-13=-3(x+2)^{2}$

$h(x)=-3(x+2)^{2}+13$

The vertex is the point (-2,13)

The x-coordinate of the vertex is -2

The axis of symmetry is x=-2

Part 4) Rank their axis of symmetry from least to greatest

1) h(x) -----> axis of symmetry -2

2) f(x) -----> axis of symmetry 0

3) g(x) -----> axis of symmetry 4

h(x),f(x),g(x)

7 0

4 years ago

Please explain how - calc ab - see attached photo

baherus [9]

Answer:

Step-by-step explanation:

Set up to different integrals that match the endpoints

so in our case it would look like

$\int\limits^0_{-2} {x} \, dx +\int\limits^1_0 {x+1} \, dx$

now it's just a matter of computing it

$\int\limits^0_{-2} {x} \, dx =x^2\\0^2-(-2)^2=4\\\int\limits^1_0 {x+1} \, dx =\frac{x^2}{2}+x\\\frac{1}{2}+1-0=\frac{3}{2}\\\frac{3}{2}+4=\frac{11}{2}$

4 0

3 years ago

Yousef is making cookies for a friend's birthday. The recipe only makes one dozen cookies, and he wants to take 4 dozen to the b

FinnZ [79.3K]

Answer:

6 and 2/3

Step-by-step explanation:

you do 1 2/3 x 4 because that is the amount of flour you need to make one batch. That is the correct answer.

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3 years ago