Re: Finding the Equation of a Parabola using the vertex and 1 point -- Mathematics Help

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Subject: Re: Finding the Equation of a Parabola using the vertex and 1 point

Author:
masnah binti abd.rahim
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Date Posted: 02:59:18 09/09/04 Thu
In reply to: QUITTNER 's message, "Re: Finding the Equation of a Parabola using the vertex and 1 point" on 09:11:49 11/10/03 Mon

>>vertex (5,12), Point (7,15)
>>I know that standard form is f(x)=a(x-h)^2+k
>>how do i plug these in to get the proper answer.
>>The book gives the answer as -3/4(x-5)^2+12
>..... We have two points (x,y), with the vertex being
>one of them. We also know that
>y=a(x-h)^2+k This is (y-k)=a*(x-h)^2
>Note that we deal here with the differences in x and
>in y, distances from the (given) vertex. Therefore
>k=the y of the vertex, and h is the x of the vertex.
>Therefore (15-12)=a*(7-5)^2
>3=a*(2)^2 and 3=a*4 giving a=3/4
>The parabola's equation is therefore for ANY x and y:
>y=(3/4)*(x-5)^2 + 12 COMPARE with the book's answer.

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[> [> [> Subject: Re: Finding the Equation of a Parabola using the vertex and 1 point

Author:
QUITTNER
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Date Posted: 10:17:49 09/09/04 Thu

masnah binti abd.rahim, WHAT IS YOUR QUESTION?

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[> [> [> Subject: Re: Finding the Equation of a Parabola

Author:
Justin
[Edit]
Date Posted: 15:55:44 02/21/05 Mon

if the problem says express each equation in the form y=a(x-h)²+k or x=a(y-k)²+h, then how do you do y=2x²-12x+6?

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[> [> [> [> Subject: Re: Finding the Equation of a Parabola

Author:
QUITTNER
[Edit]
Date Posted: 10:00:46 02/22/05 Tue

>>> if the problem says express each equation in the form y=a(x-h)²+k or x=a(y-k)²+h, then how do you do y=2x²-12x+6?
..... First you selcet the proper equation. Here the left side is y, therefore use y=a(x-h)^2+k. Expand this to get
y=a*(x^2-2hx+h^2) + k or
y=a(x^2) - 2ahx +a(h^2) + k (1) We also know
y=2x^2) - 12x + 6 (2)
Compare the coeficients of equation (1) with those of (2):
a=2 4h=12, h=3 18+k=6, k=-12

Always check your answers:
y=2*(x-3)^2 - 12 = 2*(x^2-6x+9) - 12 =
y=2*(x^2)-12x+18-12 OK

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>>>vertex (5,12), Point (7,15) >>>I know that standard form is f(x)=a(x-h)^2+k >>>how do i plug these in to get the proper answer. >>>The book gives the answer as -3/4(x-5)^2+12 >>..... We have two points (x,y), with the vertex being >>one of them. We also know that >>y=a(x-h)^2+k This is (y-k)=a*(x-h)^2 >>Note that we deal here with the differences in x and >>in y, distances from the (given) vertex. Therefore >>k=the y of the vertex, and h is the x of the vertex. >>Therefore (15-12)=a*(7-5)^2 >>3=a*(2)^2 and 3=a*4 giving a=3/4 >>The parabola's equation is therefore for ANY x and y: >>y=(3/4)*(x-5)^2 + 12 COMPARE with the book's >answer.

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