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This graph represents a quadratic function. What is the function’s equation written in factored form and in vertex form?

creativ13 [48]

Answer:

Part a) The function’s equation written in vertex form is

$f(x)=2(x-2)^2-8$

Part b) The function’s equation written in factored form is equal to

$f(x)=2x(x-4)$

Step-by-step explanation:

Part a) What is the function’s equation written in vertex form?

we know that

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

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

where

a is a coefficient

(h,k) is the vertex

Looking at the graph

The vertex is the point (2,-8)

substitute

$f(x)=a(x-2)^2-8$

Find the value of the coefficient a

take one point from the graph

(0,0)

substitute in the equation

$0=a(0-2)^2-8\\0=4a-8\\4a=8\\a=2$

therefore

The function’s equation written in vertex form is

$f(x)=2(x-2)^2-8$

Part b) What is the function’s equation written in factored form?

we know that

The equation of a vertical parabola written in factored form is equal to

$f(x)=a(x-x_1)(x-x_2)$

where

a is a coefficient

x_1 and x_2 are the zeros or x-intercepts of the function

Remember that the x-intercept is the value of x when the value of the function is equal to zero

Looking at the graph

The zeros or x-intercepts of the function are

x=0 and x=4

so

$f(x)=a(x-0)(x-4)$

$f(x)=ax(x-4)$

Find the value of the coefficient a

take one point from the graph

(2,-8)

substitute

$-8=a(2)(2-4)\\-8=-4a\\a=2$

therefore

The function’s equation written in factored form is equal to

$f(x)=2x(x-4)$

4 0

3 years ago

Jacques deposited $1900 into an account that earns 4% interest. After t year, jaques has $3875.79in the account. How long was th

Sladkaya [172]

Deposit = $1900
Amount After interest = $3875.79
% interest = 4%
Interest = 1975.79

Time For Interest Period

4/100 × 1900 × t = 1975.79
76 t = 1975.79
=26 years

Answer = 26years

5 0

3 years ago

Find the volume make it an improper fraction then a mixed number please do a step by step explanation and I will give you brainl

Andrews [41]

Answer:

8463/32=264 15/32

Step-by-step explanation:

Let's make every fraction improper first.

7 3/4=31/4

5 2/8=42/8

6 1/2=13/2

Simplify 42/8

42/8=21/4

21/4

31/4

13/2=26/4

21/14*31/4*26/4=(21*31*26)/64=16926/64=8463/32

3 0

2 years ago

In a football tournament, the Bees scored 9 less than three times as many points as the Hornets. The Wasps scored 28 more points

Elina [12.6K]

Given:

Bees scored 9 less than three times as many points as the Hornets.

Wasps scored 28 more points than the Hornets.

Together the three teams scored 184 points.

To find:

The required equation for this scenario.

Step-by-step explanation:

Let x represent the number of points scored by the Hornets.

Bees scored 9 less than three times as many points as the Hornets.

Bees score = 3x-9

Wasps scored 28 more points than the Hornets.

Wasps score = x+28

Together the three teams scored 184 points.

$(3x-9)+x+(x+28)=184$

Therefore, the required equation is $(3x-9)+x+(x+28)=184$ .

3 0

3 years ago

The sum of three consecutive odd integers is-219. What is the first number in the set?

Alex73 [517]

Answer:

-75

Step-by-step explanation:

Let us consider the first odd number to be 'x'.

Thus:

1st odd number: x
2nd odd number: x+2
3rd odd number: x+3

According to the question, the sum of these three consecutive ODD numbers should be equal to -219

So,

x + x + 2 + x + 4 = -219

3x + 6 = -219

3x = -225

x = -75

3 0

3 years ago