Answer:
The answer is:
[tex]f(x)=2x^{2}-8x+6[/tex]
Step-by-step explanation:
The equation of a parabola in the intercept form is given by:
[tex]y=a(x-p)(x-q)[/tex]
Where:
p and q are x-intercepts
Now, we know the parabola intercepts at x=1 and x=3.
So we will have:
[tex]y=a(x-1)(x-3)[/tex]
Using the point (-1,16) we could find the value of a.
[tex]16=a(-1-1)(-1-3)[/tex]
[tex]16=a(-2)(-4)[/tex]
[tex]16=8a[/tex]
[tex]a=2[/tex]
Therefore, the equation is:
[tex]y=2(x-1)(x-3)[/tex]
[tex]y=2(x^{2}-4x+3)[/tex]
[tex]y=2x^{2}-8x+6[/tex]
The answer is:
[tex]f(x)=2x^{2}-8x+6[/tex]
I hope it helps you!
