Question

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

Answer 1

1/16

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.