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4 years ago

How to identify the vertex of a quadratic function

1 answer:

6 0

Plug the x-value into the original equation to get the y-value. Now that you know the x-value, just plug it in to the original formula for the y value. You can think of the formula for finding the vertex of a quadratic function as being (x, y) = [(-b/2a), f(-b/2a)].

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Find the first three iterates of the function f(z) = z2 + c with a value of c = 2 - 3i and an initial value of z0 = 1 + 2i.

Artist 52 [7]

Answer:

Step-by-step explanation:

We have: (I rewrote the function)

$f(z_n)={z_{n-1}} ^2+c$

Given that:

$\displaystyle c=2-3i \text{ and } z_0 = 1 + 2 i$

The first iterate will be:

$\displaystyle \begin{aligned} f(z_1)&=(z_0)^2+c \\ &=(1+2i)^2+(2-3i) \\ &= (1+4i+4i^2)+(2-3i) \\ &=1+4i-4+2-3i \\ &=-1+i \end{aligned}$

The second iterate will be:

$\begin{aligned}f(z_2) &=(z_1)^2+c\\ &=(-1+i)^2+(2-3i) \\&= (1-2i+i^2)+(2-3i) \\&=1-2i-1+2-3i \\&=2-5i \end{aligned}$

And the third iterate will be:

$\begin{aligned} f(z_3)&=(z_2)^2+c\\ &=(2-5i)^2+(2-3i) \\ &=(4-20i+25i^2)+(2-3i) \\ &=4-20i-25+2-3i \\ &=-19-23i \end{aligned}$

Hence, our answer is C.

3 0

3 years ago

Jack drove 150 miles in 3 hours. at that rate, how long will it taketo drive 400 miles

Tema [17]

150mi/3hrs = 50mph
400/50 = 8 hours
Check:
8hours * 50mi = 400 miles traveled

5 0

3 years ago

Read 2 more answers

The circumference of one of the smaller circles is 12pie cm. Find the circumference of the larger circle.. . A. 12pie cm. B. 24p

Temka [501]

There exists a similar question that would lead to the relationship of the given circumference to the unknown value. The radius of the larger circle is 12 cm. The formula for determining the circumference is,
C = 2πr
Substituting the known value,
C = 2π x 12 cm = 24π cm
Thus, the answer is letter B.

4 0

3 years ago

What’s a problem with no solution

Free_Kalibri [48]

When a problem has no solution you'll end up with a statement that's <em>false</em>. For example: 0=1 This is false because we know zero can't equal one. Therefore we can conclude that the problem has no solution.

6 0

2 years ago

Read 2 more answers

Write an expression to represent the area of the shaded region.

Blababa [14]

Answer:

(6)7+

Step-by-step explanation:

6 0

3 years ago