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3 years ago

Write the Quadratic Formula

Mathematics

1 answer:

Evgen [1.6K]3 years ago

3 0

Answer:

$y=x^2-4$

Step-by-step explanation:

we know that

The function of the graph is a vertical parabola open upward

The vertex is a minimum

The equation of a vertical parabola in vertex form is equal to

$y=a(x-h)^2+k$

where

a is a coefficient

(h,k) is the vertex

In this problem

Looking at the graph

The vertex is the point (0,-4)

substitute

$y=a(x-0)^2-4$

$y=ax^2-4$

To determine the value of "a" take a point in the graph

I take the point (3,5)

substitute the value of x and the value of y and solve for a

$5=a(3)^2-4\\9a=5+4\\9a=9\\a=1$

therefore

The equation of the quadratic function is

$y=x^2-4$

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What is the value of y in the sequence below? 2,y,18, -54,162,

snow_lady [41]

First, let's check if the sequence is geometric or arithmetric.

If arithmetric, the sequence will have common difference.

Arithmetric

$\displaystyle \large{a_{n + 1} - a_n = d}$

d stands for a common difference. Common Difference means that sequences must have same difference after subtracting.

Geometric

$\displaystyle \large{ \frac{a_{n + 1}}{a_n} = r}$

r stands for a common ratio.

To find the value of y, you can check the sequence. If we try subtracting the sequences, the differences are different. That means the sequences are not arithmetric. That only leaves the geometric sequence.

Let's check by dividing sequences.

We have:

2,y,18,-54,162,...

Let's check by divide -54 by 18 and 162 by -54. We need to divide more than one so we can prove that the sequence is geometric.

$\displaystyle \large{ \frac{ - 54}{18} = - 3 } \\ \displaystyle \large{ \frac{ 162}{ - 54} = - 3}$

Hence, the sequence is geometric.

Because the common ratio is -3. Let these be the following:

$\displaystyle \large{ a_{n + 1} = y } \\ \displaystyle \large{ a_n = 2 } \\ \displaystyle \large{ r = - 3 }$

From the:

$\displaystyle \large{ \frac{a_{n + 1}}{a_n} = r}$

Substitute the values in.

$\displaystyle \large{ \frac{y}{2} = - 3}$

Multiply the whole equation by 2 to isolate y.

$\displaystyle \large{ \frac{y}{2} \times 2 = - 3 \times 2} \\ \displaystyle \large{ y = - 6}$

Therefore, the value of y is -6.

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Answer:

im in middle school and im trying to figure this out as well

Step-by-step explanation:

sorry if i get it i will tell you

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Step-by-step explanation:

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Explanation:
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