Write the equation of a parabola with x-intercept at (3,0) and (9,0) the passes through the point (10,-7)

The equation of the parabola is y = -x² + 12x - 27

Parabola is the locus of a point such that the same distance from a fixed line, called the directrix, and a fixed point (the focus) is the same.

The equation of a parabola is in quadratic form. Hence it is given as:

y = ax² + bx + c

At point (3, 0):

0 = a(3²) + b(3) + c

9a + 3b + c = 0      (1)

At point (9, 0):

0 = a(9²) + b(9) + c

81a + 9b + c = 0      (2)

At point (10, -7):

-7 = a(10²) + b(10) + c

100a + 10b + c = -7      (3)

Solving equations 1, 2, 3 gives: a = -1, b = 12, c = -27

The equation of the parabola is hence y = -x² + 12x - 27

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Step-by-step explanation:

The general equation of the parabola is

As the parabola passes through

Subtract (i) from (ii)

Also, the parabola passes through ,

Subtract (i) from (iii)

Put

Put in

Put in (i)

So, equation is

complete the steps to find the area of the trapezoid.

area of rectangle = 256   square units

area of triangle 1 = 24  square units

area of triangle 2 = 16  square units

area of triangle 3 =   96 square units

area of trapezoid = 120  square units

step-by-step explanation:

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step-by-step explanation: