Answer:
The equation of the parabola is:
[tex]y=3x^2-48x+178[/tex]Explanation:
The equation of a parabola is written as:
[tex]y=a(x-h)^2+k[/tex]Where h and k are coordinates of the vertex of the parabola, and x and y are the coordinates of the point.
h = 8, k = -14, x = 5, y = 13
Substituting these values into the equation, we have
[tex]13=a(5-8)^2+(-14)[/tex]Solving this, we will have the value for a.
[tex]\begin{gathered} 13=a(-3)^2-14 \\ \text{Add 14 to both sides} \\ 13+14=a(-3)^2-14+14 \\ 27=a(-3)^2 \\ 27=9a \\ \text{Divide both sides by 9} \\ a=\frac{27}{9}=3 \end{gathered}[/tex]Using this value of a, the equation becomes
[tex]\begin{gathered} y=3(x-8)^2-14 \\ =3(x^2-16x+64)-14 \\ =3x^2-48x+192-14 \\ y=3x^2-48x+178 \end{gathered}[/tex]