All categories

2 years ago

PLEASE HELP find the vertex of f(x)=x^2+2x+3 (make sure you show your work)

Mathematics

1 answer:

kotegsom [21]2 years ago

4 0

Answer:

(- 1, 2)

Step-by-step explanation:

Given a quadratic in standard form y = ax² + bx + c : a ≠ 0

Then the x- coordinate of the vertex is

$x_{vertex}$ = - $\frac{b}{2a}$

f(x) = x² + 2x + 3 ← is in standard form

with a = 1 and b = 2, hence

$x_{vertex}$ = - $\frac{2}{2}$ = - 1

Substitute x = - 1 into f(x) for corresponding value of y

f(- 1) = (- 1)² + 2(- 1) + 3 = 1 - 2 + 3 = 2

vertex = (- 1, 2 )

You might be interested in

***Please show all work and give explanation*** I'm in algebra 2 and we are working with matrices. So that would be the preferre

Katarina [22]

Answer:

The Washington High School won the meet by scoring 162 points

The Johnson High School came in second place by scoring 159 points, 3 points less than the winner.

Step-by-step explanation:

Arithmetics

We need to perform a number of basic arithmetics operations and derive conclusions out of the results.

We know that

10 points are awarded for each first-place finish
8 points are awarded for each second-place finish
7 points are awarded for each third-place finish

* Washington High School had 10 first-place finishes, 6 second-place finishes, and 2 third-place finishes.

Total points: 10*10+6*8+2*7=162 total points

* Johnson High School had 8 first-place finishes, 9 second-place finishes, and 1 third-place finish.

Total points: 8*10+9*8+1*7=159 total points

* Roosevelt High School had 4 first-place finishes, 5 second-place finishes, and 4 third-place finishes.

Total points: 4*10+5*8+4*7=108 total points

* Lewis High School had 3 first-place finishes, 3 second-place finishes, and 6 third-place finishes.

Total points: 3*10+3*8+6*7=96 total points

The Washington High School won the meet by scoring 162 points

The Johnson High School came in second place by scoring 159 points, 3 points less than the winner.

8 0

2 years ago

С (2x + 19) (3х + 8) А

soldier1979 [14.2K]

Answer:

x=9

Step-by-step explanation:

step one pull out the factors

3x - 27 = 3 • (x - 9)

and step two: Equations which are never true

2.1 Solve : 3 = 0

This equation has no solution.

A a non-zero constant never equals zero.

so x-9=0 and add both sides to 9 and to equal 9

5 0

2 years ago

Help with graph question

Gala2k [10]

The first thing we are going to do to graph our equation is solve them for $y$ :
For our first equation:
$4x-5y=50$
$-5y=20-4x$
$y= \frac{4}{5} x-4$
For our second equation:
$3x+y=-4$
$y=-3x-4$

Now, we just need to use the graphing utility to graph our equations:
$y= \frac{4}{5} x-4$
$y=-3x-4$

We can conclude that the graph of the equations is: