The graph of a quadratic function is represented by the table. Х
f(x)
6
-2
7
4
8
6
9
4
10
-2
What is the equation of the function in vertex form?
Substitute numerical values for a, h, and k.

The equation of the function in vertex form is f(x) = -2·(x - 8)² + 6

Step-by-step explanation:

The given values are

x,            f(x)

6,             -2

7,              4

8,              6

9,              4

10,            -2

The equation of the function in vertex form is given as follows;

f(x) = a × (x - h)² + k

To find the values of a, h, and k, we proceed as follows;

When x = 6, f(x) = -2

We have;

-2 = a × (6 - h)² + k = (h²-12·h+36)·a + k(1)

When x = 7, f(x) = 4

We have;

4 = a × ( 7- h)² + k = (h²-14·h+49)·a + k(2)

When x = 8, f(x) = 6(3)

We have;

6 = a × ( 8- h)² + k

When x = 9, f(x) = 4.

We have;

4 = a × ( 9- h)² + k (4)

When x = 10, f(x) = -2(5)

We have;

-2 = a × ( 10- h)² + k

Subtract equation (1) from (2)

4-2 =  a × ( 7- h)² + k - (a × (6 - h)² + k ) = 13·a - 2·a·h(6)

Subtract equation (4) from (2)

a × ( 9- h)² + k - a × ( 7- h)² + k

32a -4ah = 0

4h = 32

h = 32/4 = 8

From equation (6) we have;

13·a - 2·a·8 = 6

-3a = 6

a = -2

From equation (1), we have;

-2 = -2 × ( 10- 8)² + k

-2 = -8 + k

k = 6

The equation of the function in vertex form is f(x) = -2·(x - 8)² + 6

the equation cos(35) =a/25 can be used to find the length of bc what is the length of bc? round to the nearest tenth

step-by-step explanation:

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.