Suppose a parabola has an axis of symmetry at x= -1, a maximum height of 6, and passes through the point (-2,1). write the equation of the parabola in vertex form

y = - 5(x + 1)^2 + 6

the equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k ) are the coordinates of the vertex and a is a multiplier

the x- coordinate of the vertex lies on the axis of symmetry and the maximum value is the y-coordinate of the vertex, hence

vertex = (- 1, 6 )

y = a(x + 1)² + 6

To find a substitute (- 2, 1) into the equation

1 = a + 6 ⇒ a = - 5

y = - 5(x + 1)² + 6 ← equation in vertex form

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}

step-by-step explanation:

this is not possible to solve with the info given.   you need at least an one angle somewhere.