Question

Question is in the image

Answer 1

Answer:

The answer is:

$f(x)=2x^{2}-8x+6$

Step-by-step 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!