Answer:
The equation of parabola is [tex]y=-\frac{5}{2}x^2+\frac{9}{2}x-4.5[/tex].
Step-by-step explanation:
Equation of a parabola is quadratic equation.
Let the equation of parabola be
[tex]y=Ax^2+Bx+C[/tex] .... (1)
The parabola contains points ( -2, -23.5), (0,-4.5), (4,-26.5).
Put (0,-4.5) in equation (1),
[tex]-4.5=A(0)^2+B(0)+C[/tex]
[tex]-4.5=C[/tex]
Put this value in equation (1).
[tex]y=Ax^2+Bx-4.5[/tex] ... (2)
Put ( -2, -23.5) and (4,-26.5) in equation (2).
[tex]-23.5=A(-2)^2+B(-2)-4.5[/tex]
[tex]-19=4A-2B[/tex] .... (3)
[tex]-26.5=A(4)^2+B(4)-4.5[/tex]
[tex]-22=16A+4B[/tex] .... (4)
On solving (3) and (4), we get
[tex]A=-\frac{5}{2}[/tex] and [tex]B=\frac{9}{2}[/tex]
Therefore the value of parabola is
[tex]y=-\frac{5}{2}x^2+\frac{9}{2}x-4.5[/tex]
