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kondaur [170]
3 years ago
7

Plot the x-intercept(s), y-intercept, vertex, and axis of symmetry for the function below.

Mathematics
2 answers:
telo118 [61]3 years ago
6 0
<span>g(x) = x^2 + 4x + 3

y-intercept:  let x=0.  Then y=3.  y-intercept is (0,3).

roots:  set g(x) = 0 and solve for x.  x=-1 and x=-3.

                                                                                       -4
axis of symmetry:  find x = -b / (2a), which here is x = ----- = -2
                                                                                        2</span>
AnnZ [28]3 years ago
6 0
<span>Given a quadratic equations:
g(x) = x</span>²<span> + 4x + 3

The equation cannot be factored as it's not a complete square.
therefore using the vertex form of a quadratic equation we will convert the equation into its vertex form and hence it's easy to graph a quadratic equation in vertex form.

The vertex for is :
g(x) = a(x - h)</span>² + k 
where,
'h' is the axis of symmetry and (h,k) is the vertex.
So from the given equation we will rewrite the equation as:
x² + 4x + 3 = 0
x² + 4x = -3
x² + 4x + (2)² = -3 + (2)²
(x + 2)² = -3 + 4
(x + 2)² = 1
(x + 2)² - 1 = 0
Hence,
h = -2
and
k = -1

Thus our line of symmetry is x = -2 and vertex is (h,k) = (-2,-1)
Now,
we will find the x intercepts,
using the equation,
(x + 2)² = 1
square root on both sides,
√(x + 2)² = √1
x + 2 = <span>± 1
x = 1 - 2
x = -1
or
x = -1 -  2
x = -3

For y-intercept put x = 0 into the real equation:
</span>g(x) = 0² + 4(0) + 3
y = 3

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-1/3 + (-7/4)<br> pls help
djverab [1.8K]

Answer:

  -25            

 ——— = -2.08333

    12  

Step-by-step explanation:

Step  1  :

           7

Simplify   —

           4

Equation at the end of step  1  :

       1           7

 (0 -  —) +  (0 -  —)

       3           4

Step  2  :

           1

Simplify   —

           3

Equation at the end of step  2  :

       1     -7

 (0 -  —) +  ——

       3     4

Step  3  :

Calculating the Least Common Multiple :

3.1    Find the Least Common Multiple

     The left denominator is :       3

     The right denominator is :       4

       Number of times each prime factor

       appears in the factorization of:

Prime

Factor   Left

Denominator   Right

Denominator   L.C.M = Max

{Left,Right}

3 1 0 1

2 0 2 2

Product of all

Prime Factors  3 4 12

     Least Common Multiple:

     12

Calculating Multipliers :

3.2    Calculate multipliers for the two fractions

   Denote the Least Common Multiple by  L.C.M

   Denote the Left Multiplier by  Left_M

   Denote the Right Multiplier by  Right_M

   Denote the Left Deniminator by  L_Deno

   Denote the Right Multiplier by  R_Deno

  Left_M = L.C.M / L_Deno = 4

  Right_M = L.C.M / R_Deno = 3

Making Equivalent Fractions :

3.3      Rewrite the two fractions into equivalent fractions

Two fractions are called equivalent if they have the same numeric value.

For example :  1/2   and  2/4  are equivalent,  y/(y+1)2   and  (y2+y)/(y+1)3  are equivalent as well.

To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.

  L. Mult. • L. Num.      -1 • 4

  ——————————————————  =   ——————

        L.C.M               12  

  R. Mult. • R. Num.      -7 • 3

  ——————————————————  =   ——————

        L.C.M               12  

Adding fractions that have a common denominator :

3.4       Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

-1 • 4 + -7 • 3     -25

———————————————  =  ———

      12            12

Final result :

 -25            

 ——— = -2.08333

 12            

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