A intersection b formula

What is the vertex and axis of symmetry for y=4x^2-12x+9?

VLD [36.1K]

Answer:

axis of symmetry x=3/2

vertex (3/2, 0)

Step-by-step explanation:

to find the axis of symmetry we use h = -b/2a

where ax^2 + bx+c

h = -(-12)/2(4)

h= 12/8

h = 3/2

the axis of symmetry is x = 3/2

the x coordinate of the vertex is h x=3/2

to find k, the y coordinate of the vertex, substitute x=3/2 into the equation

y=4x^2-12x+9

y=4(3/2) ^2-12(3/2)+9

= 4 (9/4) - 6*3 +9

= 9-18+9

= 0

the vertex (3/2, 0)

4 0

3 years ago

I need help please help me with this

aliya0001 [1]

Step-by-step explanation:

first you do 8 * 1 what's 5 once you do that you'll get your answer do your other question to transfer that and I believe your answers up

7 0

3 years ago

The office manager of a small office ordered 140 packs of printer paper based on average daily use, she knows that the paper wil

Mandarinka [93]

slope intercept form is y=mx+b

So slope intercept form is The office manager of a small office ordered 140 packs of printer paper based on average daily use, she knows that the paper will last about 80 days

(A) Lets make a table

X axis represents the Number of days paper used

y axis represents the packs of printer paper used

x y

days packs of printer paper used

0 0 (0 days , 0 packs used)

80 140 (in 80 days , 140 packs paper used)

The graph is attached below

(B) To find Equation of a line we use points (0,0) and (80,140)

$slope = \frac{y_2-y_1}{x_2-x_1} = \frac{140-0}{80-0} = \frac{7}{4}$

y intecept is (0,0)

so b= 4

Slope intercept form of a line i y=mx + b

m is the slope and b is the y intercept

So slope intercept form of line becomes

$y= \frac{7}{4} x$

Standard form is Ax + By =C

$y= \frac{7}{4} x$

Multiply both sides by 4

4y = 7x

Now subtract 7x on both sides

-7x + 4y =0 is the standard form

(c) To find packs of printer paper the manager expect to have after 30 days, Plug in 30 for x and find out y

$y= \frac{7}{4} x$

$y= \frac{7}{4}(30)= 52.5$

Total 140 packs of printer paper

52.5 packs of paper used

Packs of paper remaining after 30 days = 140- 52.5= 87.5

8 0

3 years ago

What is the equation of a line perpendicular to y=-2/5X-1 that passes through (2,-8)

AysviL [449]

Answer:

$y=\frac{5}{2}x-13$

Step-by-step explanation:

Given the equation

$y=-\frac{2}{5}x-1$

comparing the equation with the slope-intercept form $y=mx+b$

Here,

m is the slope

b is the intercept

so the slope of the line is m = -2/5

As we know that the slope of the perpendicular line is basically the negative reciprocal of the slope of the line,

so the slope of the perpendicular line will be: 5/2

Therefore, the point-slope form of the equation of the perpendicular line that goes through (2,-8) is:

$y-y_1=m\left(x-x_1\right)$

$y-\left(-8\right)=\frac{5}{2}\left(x-2\right)$

$y+8=\frac{5}{2}\left(x-2\right)$

subtract 8 from both sides

$y+8-8=\frac{5}{2}\left(x-2\right)-8$

$y=\frac{5}{2}x-13$

8 0

3 years ago

Y= x^2-4x+3 in vertex form

Karolina [17]

Answer:

$y=(x-2)^2-1$

Step-by-step explanation:

<u>Complete the square</u>

<u /> $y=x^2-4x+3\\\\y+1=x^2-4x+3+1\\\\y+1=x^2-4x+4\\\\y+1=(x-2)^2\\\\y=(x-2)^2-1$

4 0

2 years ago