The vertex of this parabola is at (3,5) when the y-value is 6 the x value -1 what is the coefficient of the squared term in the parabolas equation

1/16

Step-by-step explanation:

Here,

Vertex =(3,5)

x= -1, y=6

Simply,eqn of parabola is given by ax^2+bx+c=y

So, coefficient of squared term (x^2) is 'a'

Therefore, we've to find the value of a

Moving on to solution:

a-b+c=6 ___(i) (by putting the given values of x and y in eqn of parabola )

We know that,

Vetex=(-b/2a, ( 4ac-b^2)/4a)

(3,5) = (-b/2a , (4ac-b^2)/4a)

Equating corresponding sides,we get

3= -b/2a

b=-6a___(ii)

Again,

5=(4ac-b^2)/4a

5=(4ac/4a) - (b^2/4a)

5= c- (36a^2/4a) (by putting value of b from eqn ii )

5= c-9a___(iii)

Now,moving back to the first eqn

a+6a+5+9a=6

16a=1

therefore,a=1/16

Hence ,the required value of coefficient of squared term is 1/16.

I tried my best to give clear explanation as much as I know. It's just we've have to find the value of a . For that, you can use any method you find easier.

answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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