Question

Question is in the image

Answer 1

The answer is:

`f(x)=2x^(2)-8x+6`

Explanation:

The equation of a parabola in the intercept form is given by:

`y=a(x-p)(x-q)`

Where:

p and q are x-intercepts

Now, we know the parabola intercepts at x=1 and x=3.

So we will have:

`y=a(x-1)(x-3)`

Using the point (-1,16) we could find the value of a.

`16=a(-1-1)(-1-3)`

`16=a(-2)(-4)`

`16=8a`

`a=2`

Therefore, the equation is:

`y=2(x-1)(x-3)`

`y=2(x^(2)-4x+3)`

`y=2x^(2)-8x+6`

The answer is:

`f(x)=2x^(2)-8x+6`

I hope it helps you!