Given:
The vertex of the parabola is (1,2).
The point passes through the parabola = (3,10).
Required:
We need to find the equation of the parabola.
Explanation:
Consider the standard form equation for the parabola.
[tex]y=a(x-h)^2+k[/tex]where (h,k) is the vertex.
Substitute (h,k) =(1,2) in the equation.
[tex]y=a(x-1)^2+2[/tex]Substitute x =3 and y=10 in the equation to find the value of a.
[tex]10=a(3-1)^2+2[/tex][tex]10=a(2)^2+2[/tex][tex]10=4a+2[/tex]Subtract 2 from both sides of the equation.
[tex]10-2=4a+2-2[/tex][tex]a=2[/tex]Substitute a =2, h=1 nad l=2 in the equation of the parabola.
[tex]y=2(x-1)^2+2[/tex][tex]\text{Use \lparen a-b\rparen}^2=a^2+b^2-2ab.[/tex][tex]y=2(x^2+1^2-2(1)(x))+2[/tex][tex]y=2(x^2+1-2x)+2[/tex][tex]y=2x^2+2\times1-2\times2x+2[/tex][tex]y=2x^2+2-4x+2[/tex][tex]y=2x^2-4x+2+2[/tex][tex]y=2x^2-4x+4[/tex]Final answer:
The standard form equation for the function:
[tex]y=2x^2-4x+4[/tex]
