Quadratic Equations

[sapphire]

Determine the equation, in factored form, of the parabola with roots at 4 and -6 that also passes through the point (1, -3).

 

[lev888]

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[nasi112]

If you could solve this problem correctly, you would understand many of the parabola's properties.

I would start by [MATH](x + a)(x + b) = 0[/MATH]

 

[HallsofIvy]

If a quadratic function has a zero at x= 4 then it has x- 4 as a factor. If it has a zero at x= -6 then it has x+ 6 as a factor. Since it is quadratic those are the only factors, involving x, that it has. It can have constant factor. What must that constant be so that when x= 1, y= -3?

 

[jonah2.0]

Beer soaked suggestion follows.

Determine the equation, in factored form, of the parabola with roots at 4 and -6 that also passes through the point (1, -3).

Google is your friend.

given 3 points find quadratic equation - Google Search

 

[Steven G]

y=A(x-r₁)(x-r₂)

 

[lex]

Determine the equation, in factored form, of the parabola with roots at 4 and -6 that also passes through the point (1, -3).

If a quadratic has roots [MATH]x=\alpha[/MATH] and [MATH]x=\beta[/MATH], then it's equation is:
[MATH]y=a(x-\alpha)(x-\beta)[/MATH], for some constant '[MATH]a[/MATH]'
You know two roots; one can be [MATH]\alpha[/MATH], one [MATH]\beta[/MATH], so you can fill in most of the equation.
To find the final bit '[MATH]a[/MATH]', use the point you have: when [MATH]x=1, y=-3[/MATH].

 

[lex]

y=A(x-r₁)(x-r₂)

More succinct!