All categories

3 years ago

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

Mathematics

1 answer:

grigory [225]3 years ago

4 0

Answer:

vertex form: f (x) = 2 * (x - 2) ^ 2 - 8

factored form: f (x) = 2 * x * (x - 4)

Step-by-step explanation:

The first thing is to calculate the equation with its vertex form, we can calculate it knowing that it is formulated in the following:

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), we replace and we are left with:

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

Now, to calculate the value of the coefficient we are going to

mark a point on the graph

, we will select (0,0)

and replacing we have:

0 = a * (0 - 2) ^ 2 - 8

0 = 4 * a - 8

a = 8/4

a = 2

Therefore, we would be left with the equation of the function written in The first thing is to calculate the equation with its vertex form, we can calculate it knowing that it is formulated in the following:

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), we replace and we are left with:

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

Now, to calculate the value of the coefficient we are going to

mark a point on the graph

, we will select (0,0)

and replacing we have:

0 = a * (0 - 2) ^ 2 - 8

0 = 4 * a - 8

a = 8/4

a = 2

Therefore, we would be left with the equation of the function written in vertex form:

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

Now for the factored form, we know it has the following structure:

f (x) = a * (x - x1) * (x - x2)

knowing that a is a coefficient

and that x1 and x2 are the zeros or x-intercepts of the function

Looking at the graph

The zeros or x-intercepts of the function are

x = 0 and x = 4

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

f (x) = a * x * (x - 4)

To calculate the value of the coefficient a, we will take the point (2, -8), we replace:

-8 = a * 2 * (2 - 4)

-8 = 4 * a - 8 * a

4 * a = 8

a = 2

we replace and we have:

f (x) = 2 * x * (x - 4) and this would be the factored form of the equation

Now for the factored form, we know it has the following structure:

f (x) = a * (x - x1) * (x - x2)

knowing that a is a coefficient

and that x1 and x2 are the zeros or x-intercepts of the function

Looking at the graph

The zeros or x-intercepts of the function are

x = 0 and x = 4

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

f (x) = a * x * (x - 4)

To calculate the value of the coefficient a, we will take the point (2, -8), we replace:

-8 = a * 2 * (2 - 4)

-8 = 4 * a - 8 * a

4 * a = 8

a = 2

we replace and we have:

f (x) = 2 * x * (x - 4) and this would be the factored form of the equation

You might be interested in

The concept and full method

marin [14]

Answer:

Step-by-step explanation:

This kinda looks like the limiting definition of a derivative.

Anyway, what we are doing with the f(2 + h) is evaluating f(x) with 2+h in place for x. That looks like this:

f(2 + h) = 2(2 + h) - 3 which simplifies to

f(2 + h) = 4 + 2h - 3 which simplifies to

2h + 1

From that we are subtracting f(2). What we are doing with that is evaluating f(x) with 2 in place for x. That looks like this:

f(2) = 2(2) - 3 which simplifies to

f(2) = 4 - 3 which simplifies to

f(2) = 1. Now put those together over h to get:

$\frac{f(2+h)-f(2)}{h}=\frac{2h+1-1}{h}=\frac{2h}{h}=2$

5 0

3 years ago

What is the slope of a line that is perpendicular to the line whose equation is ax+by=c?

Oksi-84 [34.3K]

The perpendicular line will have a slope of b/a.

To find this, we first have to solve our equation for slope intercept form.

ax + by = c ----> subtract ax

by = -ax + c ----> divide by b

y = -a/bx + c/b.

So we know the slope of this equation to be -a/b. Since perpendicular lines have opposite and reciprocal slopes, we know we can simply flip the fraction and make it a negative to get the new slope of b/a.

6 0

3 years ago

mica and denise are reading the same novel. mica has read 1/2 of the novel, and denise has read 1/3 of the novel. how much more

vovangra [49]

You convert the fractions into 6ths. So 1/3. You would multiply both parts by 2 (top and bottom denominators) and that would be 2/6. 1/2 of 6 is 3/6. So the answer would be 1/6

7 0

3 years ago

Read 2 more answers

What is the rounding off of 123.5201 ,424.9832 ,675.0608 ,1247.0057 & 5653.5974

sleet_krkn [62]

rounding off of 123.5201 is 123.5

rounding off of 424.9832 is 425

rounding off of 675.0608 is 675.1

rounding off of 1247.0057 is 1247

rounding off of 5653.5974 is 5653.6

here we have rounded off to first decimal place

one point to note that we can just approximate to get the rounded off value. We have to follow several rules, like we should increase the last digit to be retained by one when the digit following it is greater than 5 and we should not

change the last digit if the digit following the last digit to be retained is less than five

4 0

3 years ago

-7 - -3(x+3)>5 how do I work this problem

charle [14.2K]

Answer:

x > 1

Step-by-step explanation:

It's actually a pretty simple algebra problem, you can pretend the > is an = for the most part. The only difference is if you ever multiply or divide by a negative you flip the direction

-7 + 3(x+3)>5 (as long as that double minus sign was accurate)

-7 + 3x + 9 > 5

2 + 3x >5

3x > 3

x > 1

Now, like I mentioned if you divide or multiply by a negative the inequality flips. so say you multiply by -1 on both sides you will get -x < -2. I just want to make sure you remember that because it can be hard to remember.

5 0

3 years ago