(Easy) For the following quadratic function, find the axis of symmetry, the vertex and the y-intercept. y = x^2 + 12x + 32

see explanation

Step-by-step explanation:

Given a quadratic in standard form , y = ax² + bx + c ( a ≠ 0 ), then

The x- coordinate of the vertex, which is also the equation of the axis of symmetry is

= -

y = x² + 12x + 32 ← is in standard form

with a = 1, b = 12 , then

= - = - 6

Substitute x = - 6 into y for corresponding y- coordinate

y = (- 6)² + 12(- 6) + 32 = 36 - 72 + 32 = - 4

Thus

equation of axis of symmetry is x = - 6

vertex = (- 6, - 4 )

To find the y- intercept , let x = 0

y = 0² + 12(0) + 32 = 32 ← y- intercept

the inequality is:

250c+180g≥950

step-by-step explanation:

let c denotes the number of days in a week   miyoko worked as a cryptographer.

and g denotes the number of days in a week she works as a geologist.

now we are given that she earns $250 for every day she works as a cryptographer,and earns $180 for every day she works as a geologist.

now miyoko's goal is to earn more than $950 this week.

hence, the inequality could be represented as:

250c+180g≥950

g(x) = 3*(8(3^(x−2))+2)

g(x) = 24 (3^(x-2) )+6

the factor is 2

step-by-step explanation:

let f(x)=8(3^(x−2)+2)

to stretch a graph by 3, it would be 3f(x)

g(x) =3f(x)

g(x) = 3*(8(3^(x−2))+2)

g(x) = 24 (3^(x-2) )+6

x     −2     0     2     4     6

f(x) 1/64 1/16   1/4     1     4

1/64 * z * z = 1/16

i multiplies by z twice because it its 2 steps from -2 to 0

1/64 z^2 = 1/16

multiply by 64 to clear the fraction on the left side

1/4 * 64 z^2 =1/16 *64

z^2 = 4

take the square root of each side

sqrt(z^2) = ±sqrt(4)

z = ±2  

we are multiplying by 2 each time.