Question

A parabola has two x intercepts at (-2 , 0) and (3 , 0) and passes through the point (5 , 10). Find the equation of this parabola. ​

Answer 1

Hi..

y = a(x + 2)(x - 3) : equation of the parabola in factored form

y = a(x + 2)(x - 3) : equation of the parabola in factored form 10 = a(5 + 2)(5 - 2) : (5 , 10) is a point on the graph of the parabola and therefore satisfies the equation of the parabola.

y = a(x + 2)(x - 3) : equation of the parabola in factored form 10 = a(5 + 2)(5 - 2) : (5 , 10) is a point on the graph of the parabola and therefore satisfies the equation of the parabola. a = 5/7: solve the above equation for a.

Answer 2

${\huge{\red{\mathfrak{answer}}}}$

The equation you want is Ax2 + Bx + C = y

Put each pair of (x,y) values into the equation.

You will get 3 simultaneous linear equations in the unknowns A, B and C.

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