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what is the equation, in standard form, of a parabola that contains the following points? ( -2, -23.5)(0,-4.5)(4,-26.5)

2 Answers

6 votes
y = -2.5x^2 + 4.5^x + -4.5
what is the equation, in standard form, of a parabola that contains the following-example-1
User Jfrobishow
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8.2k points
1 vote

Answer:

The equation of parabola is
y=-(5)/(2)x^2+(9)/(2)x-4.5.

Explanation:

Equation of a parabola is quadratic equation.

Let the equation of parabola be


y=Ax^2+Bx+C .... (1)

The parabola contains points ( -2, -23.5), (0,-4.5), (4,-26.5).

Put (0,-4.5) in equation (1),


-4.5=A(0)^2+B(0)+C


-4.5=C

Put this value in equation (1).


y=Ax^2+Bx-4.5 ... (2)

Put ( -2, -23.5) and (4,-26.5) in equation (2).


-23.5=A(-2)^2+B(-2)-4.5


-19=4A-2B .... (3)


-26.5=A(4)^2+B(4)-4.5


-22=16A+4B .... (4)

On solving (3) and (4), we get


A=-(5)/(2) and
B=(9)/(2)

Therefore the value of parabola is


y=-(5)/(2)x^2+(9)/(2)x-4.5

what is the equation, in standard form, of a parabola that contains the following-example-1
User Mohammad Nouri
by
7.6k points

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