Find the coordinates of the vertex of the following parabola algebraically. Write your answer as an (x, y) point.
y=4x^2+24x-40

Please help me out, need it fast it’s timed. Thanks

(-3,-76)

Step-by-step explanation:

(22x2 +  24x) -  40  = 0

STEP

2

:

STEP

3

:

Pulling out like terms

3.1     Pull out like factors :

  4x2 + 24x - 40  =   4 • (x2 + 6x - 10)

Trying to factor by splitting the middle term

3.2     Factoring  x2 + 6x - 10

The first term is,  x2  its coefficient is  1 .

The middle term is,  +6x  its coefficient is  6 .

The last term, "the constant", is  -10

Step-1 : Multiply the coefficient of the first term by the constant   1 • -10 = -10

Step-2 : Find two factors of  -10  whose sum equals the coefficient of the middle term, which is   6 .

     -10    +    1    =    -9

     -5    +    2    =    -3

     -2    +    5    =    3

     -1    +    10    =    9

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Equation at the end of step 3:

 4 • (x2 + 6x - 10)  = 0

STEP 4:

Equations which are never true:

4.1      Solve :    4   =  0

answer:  

step-by-step explanation:

here x represents the height of the pole,

and, the height of the shadow of the pole is 12 feet.

also, the angle of elevation from the top of the pole is 40°,

therefore,

by the low of sine,

which is the required equation for finding the value of x,

the simplified form is

step-by-step explanation:

we want to simplify the expression,

let us change the middle bar to a normal division sign to obtain,

we multiply the first fraction by the reciprocal of the second fraction to obtain,

we factor to obtain,

we cancel the common factors to get,

we simplify to get,

the correct answer is b