Mathematics, 11.10.2021 18:00 sheilaaguilar2014

Given the vertex (2, -1 )and the point(0,7), write the vertex form equation of the quadratic function
Pls help!!!

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Answer from: gungamer720

f(x) = 2(x - 2)² - 1

Step-by-step explanation:

Given the vertex, (2, -1) and the point, (0, 7), we can plug these values into the vertex form of the quadratic function:

f(x) = a(x - h)² + h

where:

vertex = (h, k)

a = determines whether the graph opens up or down, and the wideness or narrowness of the parabola.

h = determines how far left or right the parent function is translated.

k = determines how far up or down the parent function is translated.

We could substitute the given values into the vertex form, and solve for the value of "a":

f(x) = a(x - h)² + h

7 = a(0 - 2)² - 1

7 = a(-2)² - 1

7 = a(4) - 1

Add 1 to both sides:

7 + 1 = a(4) - 1 + 1

8 = 4a

Divide both sides by 4 to solve for a:

8/4 = 4a/4

2 = a

Since a = 2, and the vertex = (2, -1) then we could plug this value into the given function:

f(x) = 2(x - 2)² -1

Attached is a screenshot of the graph where it contains the given points.

Please mark my answers as the Brainliest, if you find my explanations helpful :)

Given the vertex (2, -1 )and the point(0,7), write the vertex form equation of the

quadratic funct

Answer from: Quest

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq and the angle ∠orq are opposite, therefore:

$m\angle opq+m\angle orq=180\°\\\\m\angle opq+ (2x + 16)\°=180\°$

then, $m\angle opq+ (2x + 16)\°=180\°$ can be used to d to calculate the measure of ∠opq

Quadrilateral opqr is inscribed in circle n, as shown below. which of the following could be used to

Answer from: Quest

$a_1 = 1$ , and

$a_{n+1} = a_n + (n + 1)$ for $n \ge 1$

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote $a_1 = 1$ , $a_2 = 3$ , $a_3 = 6$ , so that we can call

1 the 1st term, 3 the 2nd term, 6 the 3rd term,etc.

note the following:

from the 1st term (1) to the 2nd term (3), we go up by 2,from the 2nd term (3) to the 3rd term (6), we go up by 3from the 3rd term (6) to the 4th term (10), we go up by 4, andfrom the 4th term (10) to the 5th term (15), we go up by 5.

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from $a_1 = 1$ , to get to $a_2 = 3$ , we add $2(=1+1)$

from $a_2 = 3$ , to get to $a_3 = 6$ , we add $3 (=2+1)$

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

$a_1 = 1$ , and $a_{n+1} = a_n +(n + 1)$ for $n \ge 1$

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Given the vertex (2, -1 )and the point(0,7), write the vertex form equation of the quadratic funct...